feat: Implement initial filtering for agent search from the home screen, enable footer navigation, and add provider stability checks.

lib/routing/app_router.dart

@@ -115,9 +115,17 @@ final routerProvider = Provider<GoRouter>((ref) {
             path: '/agents/search',
             pageBuilder: (context, state) {
               final query = state.uri.queryParameters['q'];
+              final typeId = state.uri.queryParameters['type'];
+              final location = state.uri.queryParameters['location'];
+              final category = state.uri.queryParameters['category'];
               return CustomTransitionPage(
                 key: state.pageKey,
-                child: AgentSearchScreen(initialQuery: query),
+                child: AgentSearchScreen(
+                  initialQuery: query,
+                  initialAgentTypeId: typeId,
+                  initialLocation: location,
+                  initialCategory: category,
+                ),
                 transitionsBuilder: _fadeTransition,
               );
             },