### Key Changes:

**AI Equipment Proposal (`functions/aiEquipmentProposal.js`):**
- Updated Gemini model to `gemini-3.1-flash-lite-preview` and updated the API key.
- Increased `MAX_TOOL_ITERATIONS` from 12 to 20.
- Added a new tool `list_equipment_by_category` to allow the AI to browse equipment when specific searches fail.
- Enhanced the system prompt with instructions to handle typos via category exploration and authorized more creative equipment suggestions based on event descriptions.
- Improved the user prompt to include more event context (name, location, notes, and options).
- Set `responseMimeType: 'application/json'` in the generation config for better reliability.
- Improved error logging and user-facing error messages for timeouts.

**UI & Pagination (`lib/views/`):**
- **ContainerFormPage**: Replaced `StreamBuilder` with a paginated list using `DataService` for equipment selection. Added a scroll controller to support infinite scrolling and updated UI colors to use the newer `withValues` API.
- **EquipmentSelectionDialog**:
    - Increased pagination limit from 25 to 50 items.
    - Implemented `_checkIfMoreItemsNeeded` logic to automatically fetch more pages if filters (like hiding conflicting items) leave the view too empty.
    - Added a `NotificationListener` to the `ListView` to trigger pagination on scroll.
    - Fixed minor encoding issues in comments.

---

### Proposed Commit Message:

feat: Mise à jour du modèle Gemini et optimisation de la sélection du matériel avec pagination

- Mise à jour du modèle d'IA vers `gemini-3.1-flash-lite-preview` et augmentation de la limite d'itérations des outils à 20.
- Ajout de l'outil `list_equipment_by_category` pour permettre à l'IA d'explorer les alternatives en cas d'échec de recherche textuelle.
- Enrichissement du prompt système et du contexte envoyé à l'IA (nom, lieu, notes et options de l'événement).
- Implémentation de la pagination dans `ContainerFormPage` pour la sélection d'équipements afin d'améliorer les performances.
- Optimisation de `EquipmentSelectionDialog` avec chargement automatique des pages suivantes si les filtres réduisent trop la liste visible.
- Passage à `withValues` pour la gestion des couleurs et amélioration de la gestion des erreurs et du logging.

em2rp/lib/views/container_form_page.dart

@@ -7,6 +7,8 @@ import 'package:em2rp/providers/container_provider.dart';
 import 'package:em2rp/providers/equipment_provider.dart';
 import 'package:em2rp/utils/debug_log.dart';
 import 'package:em2rp/utils/id_generator.dart';
+import 'package:em2rp/services/data_service.dart';
+import 'package:em2rp/services/api_service.dart';
 
 class ContainerFormPage extends StatefulWidget {
   final ContainerModel? container;
@@ -635,23 +637,86 @@ class _EquipmentSelectorDialog extends StatefulWidget {
 
 class _EquipmentSelectorDialogState extends State<_EquipmentSelectorDialog> {
   final TextEditingController _searchController = TextEditingController();
+  final ScrollController _scrollController = ScrollController();
+  final DataService _dataService = DataService(FirebaseFunctionsApiService());
+
   EquipmentCategory? _filterCategory;
   String _searchQuery = '';
   late Set<String> _tempSelectedIds;
 
+  final List<EquipmentModel> _paginatedEquipments = [];
+  bool _isLoadingMore = false;
+  bool _hasMoreEquipments = true;
+  String? _lastEquipmentId;
+
   @override
   void initState() {
     super.initState();
     // Créer une copie temporaire des IDs sélectionnés
     _tempSelectedIds = Set<String>.from(widget.selectedIds);
+    _scrollController.addListener(_onScroll);
+    _loadNextPage();
   }
 
   @override
   void dispose() {
     _searchController.dispose();
+    _scrollController.dispose();
     super.dispose();
   }
 
+  void _onScroll() {
+    if (_isLoadingMore) return;
+    if (_scrollController.hasClients &&
+        _scrollController.position.pixels >= _scrollController.position.maxScrollExtent - 300) {
+      if (_hasMoreEquipments) {
+        _loadNextPage();
+      }
+    }
+  }
+
+  Future<void> _loadNextPage() async {
+    if (_isLoadingMore || !_hasMoreEquipments) return;
+    setState(() => _isLoadingMore = true);
+
+    try {
+      final result = await _dataService.getEquipmentsPaginated(
+        limit: 50,
+        startAfter: _lastEquipmentId,
+        searchQuery: _searchQuery.isNotEmpty ? _searchQuery : null,
+        category: _filterCategory != null ? equipmentCategoryToString(_filterCategory!) : null,
+        sortBy: 'id',
+        sortOrder: 'asc',
+      );
+
+      final newEquipments = (result['equipments'] as List<dynamic>)
+          .map((data) => EquipmentModel.fromMap(data as Map<String, dynamic>, data['id'] as String))
+          .toList();
+
+      if (mounted) {
+        setState(() {
+          _paginatedEquipments.addAll(newEquipments);
+          _hasMoreEquipments = result['hasMore'] as bool? ?? false;
+          _lastEquipmentId = result['lastVisible'] as String?;
+          _isLoadingMore = false;
+        });
+      }
+    } catch (e) {
+      if (mounted) {
+        setState(() => _isLoadingMore = false);
+      }
+    }
+  }
+
+  Future<void> _reloadData() async {
+    setState(() {
+      _paginatedEquipments.clear();
+      _lastEquipmentId = null;
+      _hasMoreEquipments = true;
+    });
+    await _loadNextPage();
+  }
+
   @override
   Widget build(BuildContext context) {
     return Dialog(
@@ -701,6 +766,7 @@ class _EquipmentSelectorDialogState extends State<_EquipmentSelectorDialog> {
                           setState(() {
                             _searchQuery = '';
                           });
+                          _reloadData();
                         },
                       )
                     : null,
@@ -709,6 +775,7 @@ class _EquipmentSelectorDialogState extends State<_EquipmentSelectorDialog> {
                 setState(() {
                   _searchQuery = value;
                 });
+                _reloadData();
               },
             ),
             const SizedBox(height: 16),
@@ -726,6 +793,7 @@ class _EquipmentSelectorDialogState extends State<_EquipmentSelectorDialog> {
                       setState(() {
                         _filterCategory = null;
                       });
+                      _reloadData();
                     },
                     selectedColor: AppColors.rouge,
                     labelStyle: TextStyle(
@@ -743,6 +811,7 @@ class _EquipmentSelectorDialogState extends State<_EquipmentSelectorDialog> {
                           setState(() {
                             _filterCategory = selected ? category : null;
                           });
+                          _reloadData();
                         },
                         selectedColor: AppColors.rouge,
                         labelStyle: TextStyle(
@@ -760,7 +829,7 @@ class _EquipmentSelectorDialogState extends State<_EquipmentSelectorDialog> {
             Container(
               padding: const EdgeInsets.all(12),
               decoration: BoxDecoration(
-                color: AppColors.rouge.withOpacity(0.1),
+                color: AppColors.rouge.withValues(alpha: 0.1),
                 borderRadius: BorderRadius.circular(8),
               ),
               child: Row(
@@ -778,86 +847,62 @@ class _EquipmentSelectorDialogState extends State<_EquipmentSelectorDialog> {
 
             // Liste des équipements
             Expanded(
-              child: StreamBuilder<List<EquipmentModel>>(
-                stream: widget.equipmentProvider.equipmentStream,
-                builder: (context, snapshot) {
-                  if (snapshot.connectionState == ConnectionState.waiting) {
-                    return const Center(child: CircularProgressIndicator());
-                  }
-
-                  if (snapshot.hasError) {
-                    return Center(child: Text('Erreur: ${snapshot.error}'));
-                  }
-
-                  var equipment = snapshot.data ?? [];
-
-                  // Filtrer par catégorie
-                  if (_filterCategory != null) {
-                    equipment = equipment.where((e) => e.category == _filterCategory).toList();
-                  }
-
-                  // Filtrer par recherche
-                  if (_searchQuery.isNotEmpty) {
-                    final query = _searchQuery.toLowerCase();
-                    equipment = equipment.where((e) {
-                      return e.id.toLowerCase().contains(query) ||
-                             (e.brand?.toLowerCase().contains(query) ?? false) ||
-                             (e.model?.toLowerCase().contains(query) ?? false);
-                    }).toList();
-                  }
-
-                  if (equipment.isEmpty) {
-                    return const Center(
-                      child: Text('Aucun équipement trouvé'),
-                    );
-                  }
-
-                  return ListView.builder(
-                    itemCount: equipment.length,
-                    itemBuilder: (context, index) {
-                      final item = equipment[index];
-                      final isSelected = _tempSelectedIds.contains(item.id);
-
-                      return CheckboxListTile(
-                        value: isSelected,
-                        onChanged: (selected) {
-                          setState(() {
-                            if (selected == true) {
-                              _tempSelectedIds.add(item.id);
-                            } else {
-                              _tempSelectedIds.remove(item.id);
-                            }
-                          });
-                        },
-                        title: Text(
-                          item.id,
-                          style: const TextStyle(fontWeight: FontWeight.bold),
-                        ),
-                        subtitle: Column(
-                          crossAxisAlignment: CrossAxisAlignment.start,
-                          children: [
-                            if (item.brand != null || item.model != null)
-                              Text('${item.brand ?? ''} ${item.model ?? ''}'),
-                            const SizedBox(height: 4),
-                            Text(
-                              _getCategoryLabel(item.category),
-                              style: TextStyle(
-                                fontSize: 12,
-                                color: Colors.grey.shade600,
-                              ),
+              child: _paginatedEquipments.isEmpty && !_isLoadingMore
+                  ? const Center(child: Text('Aucun équipement trouvé'))
+                  : ListView.builder(
+                      controller: _scrollController,
+                      itemCount: _paginatedEquipments.length + (_isLoadingMore ? 1 : 0),
+                      itemBuilder: (context, index) {
+                        if (index == _paginatedEquipments.length) {
+                          return const Center(
+                            child: Padding(
+                              padding: EdgeInsets.all(8.0),
+                              child: CircularProgressIndicator(),
                             ),
-                          ],
-                        ),
-                        secondary: Icon(
-                          _getCategoryIcon(item.category),
-                          color: AppColors.rouge,
-                        ),
-                        activeColor: AppColors.rouge,
-                      );
-                    },
-                  );
-                },
-              ),
+                          );
+                        }
+
+                        final item = _paginatedEquipments[index];
+                        final isSelected = _tempSelectedIds.contains(item.id);
+
+                        return CheckboxListTile(
+                          value: isSelected,
+                          onChanged: (selected) {
+                            setState(() {
+                              if (selected == true) {
+                                _tempSelectedIds.add(item.id);
+                              } else {
+                                _tempSelectedIds.remove(item.id);
+                              }
+                            });
+                          },
+                          title: Text(
+                            item.id,
+                            style: const TextStyle(fontWeight: FontWeight.bold),
+                          ),
+                          subtitle: Column(
+                            crossAxisAlignment: CrossAxisAlignment.start,
+                            children: [
+                              if (item.brand != null || item.model != null)
+                                Text('${item.brand ?? ''} ${item.model ?? ''}'),
+                              const SizedBox(height: 4),
+                              Text(
+                                _getCategoryLabel(item.category),
+                                style: TextStyle(
+                                  fontSize: 12,
+                                  color: Colors.grey.shade600,
+                                ),
+                              ),
+                            ],
+                          ),
+                          secondary: Icon(
+                            _getCategoryIcon(item.category),
+                            color: AppColors.rouge,
+                          ),
+                          activeColor: AppColors.rouge,
+                        );
+                      },
+                    ),
             ),
 
             // Boutons d'action
@@ -945,4 +990,7 @@ class _EquipmentSelectorDialogState extends State<_EquipmentSelectorDialog> {
         return Icons.category;
     }
   }
-}
+}
+
+
+