refactor: /simplify — 22 fixes from 3-agent code review

Critical:
- Fix MXC URI resolution: all avatars/images now resolve mxc:// to HTTP
- Sync persistence: only write changed rooms, batch message upserts
- lastActivityAt uses room.lastEvent.originServerTs, not creation time

High:
- Shared MatrixAvatar widget replaces 6 duplicate implementations
- CallScreen decodes roomId before LiveKit JWT fetch
- Decline button actually dismisses incoming call overlay
- EventTypes constants replace raw string literals
- LiveKitService uses lazy auth reads, onDispose disconnects

Medium:
- CallController is keepAlive with timer/room cleanup
- authRepository is keepAlive (used from keepAlive notifier)
- StreamController not closed in stopListening (crash fix)
- Index on messages.roomId for query performance
- 400ms debounce on user search
- Static DateFormat in MessageBubble
- Hardcoded strings replaced with AppConfig refs
- Duplicate isDirectMessage field removed from RoomModel
- E2EE profile claim corrected to Phase 3

Shared utilities:
- lib/shared/widgets/matrix_avatar.dart
- lib/shared/utils/mxc_url.dart
- lib/shared/utils/room_preview.dart
- lib/shared/utils/matrix_id.dart

rawJson column removed (unused, caused main-thread jsonEncode)
Schema migrated to v2 with roomId index.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

lib/features/rooms/presentation/user_search_dialog.dart

@@ -1,7 +1,9 @@
-// Version: 1.1.0 | Created: 2026-04-01
+// Version: 1.2.0 | Created: 2026-04-01 | Updated: 2026-04-02
 // User search dialog — search Matrix user directory and start a DM.
 // Triggered from the rooms screen "New message" button.
 
+import 'dart:async';
+
 import 'package:flutter/material.dart';
 import 'package:flutter_riverpod/flutter_riverpod.dart';
 import 'package:go_router/go_router.dart';
@@ -9,6 +11,8 @@ import 'package:matrix/matrix_api_lite.dart' show Profile;
 import 'package:riverpod_annotation/riverpod_annotation.dart';
 
 import '../../../core/network/matrix_client.dart';
+import '../../../shared/utils/mxc_url.dart';
+import '../../../shared/widgets/matrix_avatar.dart';
 
 part 'user_search_dialog.g.dart';
 
@@ -47,13 +51,22 @@ class _UserSearchDialogState extends ConsumerState<_UserSearchDialog> {
   final _controller = TextEditingController();
   String _searchTerm = '';
   bool _isStartingDm = false;
+  Timer? _debounce;
 
   @override
   void dispose() {
+    _debounce?.cancel();
     _controller.dispose();
     super.dispose();
   }
 
+  void _onSearchChanged(String val) {
+    _debounce?.cancel();
+    _debounce = Timer(const Duration(milliseconds: 400), () {
+      if (mounted) setState(() => _searchTerm = val);
+    });
+  }
+
   Future<void> _startDm(String userId) async {
     if (_isStartingDm) return;
     setState(() => _isStartingDm = true);
@@ -112,10 +125,10 @@ class _UserSearchDialogState extends ConsumerState<_UserSearchDialog> {
                 controller: _controller,
                 autofocus: true,
                 decoration: const InputDecoration(
-                  hintText: 'Search by name or user ID…',
+                  hintText: 'Search by name or user ID...',
                   prefixIcon: Icon(Icons.search),
                 ),
-                onChanged: (val) => setState(() => _searchTerm = val),
+                onChanged: _onSearchChanged,
               ),
             ),
 
@@ -160,6 +173,7 @@ class _SearchResults extends ConsumerWidget {
   Widget build(BuildContext context, WidgetRef ref) {
     final resultsAsync = ref.watch(searchUsersProvider(term));
     final theme = Theme.of(context);
+    final client = ref.watch(matrixClientProvider);
 
     return resultsAsync.when(
       loading: () => const Center(child: CircularProgressIndicator()),
@@ -186,24 +200,13 @@ class _SearchResults extends ConsumerWidget {
           itemBuilder: (context, index) {
             final profile = profiles[index];
             final displayName = profile.displayName ?? profile.userId;
-            final initials = displayName.isNotEmpty
-                ? displayName[0].toUpperCase()
-                : '?';
 
             return ListTile(
-              leading: profile.avatarUrl != null
-                  ? CircleAvatar(
-                      backgroundImage: NetworkImage(
-                        profile.avatarUrl.toString(),
-                      ),
-                    )
-                  : CircleAvatar(
-                      backgroundColor: theme.colorScheme.primary.withAlpha(51),
-                      child: Text(
-                        initials,
-                        style: TextStyle(color: theme.colorScheme.primary),
-                      ),
-                    ),
+              leading: MatrixAvatar(
+                name: displayName,
+                avatarUrl: resolveMxcUrl(client, profile.avatarUrl),
+                radius: 20,
+              ),
               title: Text(displayName),
               subtitle: Text(
                 profile.userId,