feat: image fullscreen viewer, public room browser

- Chat: tap any image to open fullscreen InteractiveViewer (pinch/zoom)
- Rooms: public room browser (Find rooms FAB + empty state button)
  searches Matrix room directory via queryPublicRooms, join from results
- Rooms: empty state now shows 'Find rooms' button to onboard new users

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

lib/features/rooms/presentation/rooms_screen.dart

@@ -1,4 +1,4 @@
-// Version: 1.4.0 | Created: 2026-04-01 | Updated: 2026-04-27
+// Version: 1.5.0 | Created: 2026-04-01 | Updated: 2026-04-27
 // Main rooms list screen with bottom navigation.
 
 import 'package:flutter/material.dart';
@@ -9,6 +9,7 @@ import '../../help/presentation/help_tab.dart';
 import '../../jitsi/presentation/conference_tab.dart';
 import '../../profile/presentation/profile_screen.dart';
 import '../../spaces/presentation/spaces_screen.dart';
+import 'public_rooms_dialog.dart';
 import 'room_tile.dart';
 import 'rooms_controller.dart';
 import 'user_search_dialog.dart';
@@ -113,6 +114,13 @@ class _RoomsScreenState extends ConsumerState<RoomsScreen> {
             )
           : null,
       body: _buildBody(),
+      floatingActionButton: _selectedIndex == 0 && !_searchActive
+          ? FloatingActionButton(
+              onPressed: () => showPublicRoomsDialog(context),
+              tooltip: 'Find rooms',
+              child: const Icon(Icons.explore_outlined),
+            )
+          : null,
       bottomNavigationBar: NavigationBar(
         selectedIndex: _selectedIndex,
         onDestinationSelected: (index) =>
@@ -233,11 +241,19 @@ class _EmptyRoomsState extends StatelessWidget {
             ),
             const SizedBox(height: 8),
             Text(
-              'Rooms you join will appear here.',
+              'Use the pencil icon above to message someone, or find '
+              'a public room to join.',
+              textAlign: TextAlign.center,
               style: theme.textTheme.bodySmall?.copyWith(
                 color: theme.colorScheme.onSurface.withAlpha(102),
               ),
             ),
+            const SizedBox(height: 20),
+            OutlinedButton.icon(
+              onPressed: () => showPublicRoomsDialog(context),
+              icon: const Icon(Icons.explore_outlined),
+              label: const Text('Find rooms'),
+            ),
           ],
         ),
       ),