feat: server-side search with debounce for professionals list

- getProfessionals() now accepts optional search param sent to ?search=
- updateCity only triggers the initial load (city no longer used as filter)
- Search field debounces 450ms before firing API call
- TextEditingController added so clear button also resets the field
- Client-side filtering removed (API now handles it and returns top 7)

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

lib/providers/professionals_provider.dart

@@ -5,25 +5,23 @@ import 'package:prosapp_web_app/services/api_service.dart';
 class ProfessionalsProvider extends ChangeNotifier {
   List<UsuarioProfesional> professionals = [];
   bool isLoading = true;
-  String? _city;
   bool _initialized = false;
   final _api = ApiService.instance;
 
   void updateCity(String? city) {
-    // Always load on first auth event; afterwards only reload when city changes.
-    if (!_initialized || _city != city) {
+    // Only used to trigger the initial load when auth becomes available.
+    if (!_initialized) {
       _initialized = true;
-      _city = city;
       getProfessionals();
     }
   }
 
-  getProfessionals() async {
+  Future<void> getProfessionals({String? search}) async {
     isLoading = true;
     notifyListeners();
     try {
-      final path = (_city != null && _city!.isNotEmpty)
-          ? '/professionals?city=${Uri.encodeComponent(_city!)}'
+      final path = (search != null && search.trim().isNotEmpty)
+          ? '/professionals?search=${Uri.encodeComponent(search.trim())}'
           : '/professionals';
       final res = await _api.get(path);
       final list = (res is Map ? res['data'] : res) as List;