fix(settings): dismiss Manage Libraries without leaving Settings

On phone layouts main_screen pushes SettingsScreen as its own route, and
that route carried no OverlaySheetHost. showAdaptive could not find one
from the tile's context, so Manage Libraries fell back to
showModalBottomSheet. The sheet also owns a focused Back handler, so a
single Android Back arrived twice — once as a key event, once as
popRoute — and the two route-based paths raced, tearing down Settings
along with the sheet.

Installs one route-local host when no enclosing host exists, and opens
the sheet from a context below it. OverlaySheetHost then holds the route
while a sheet is open and deduplicates the key path, so one Back closes
only the sheet.

lib/screens/settings/settings_screen.dart

@@ -39,6 +39,7 @@ import '../../widgets/desktop_app_bar.dart';
 import '../../widgets/dialog_action_button.dart';
 import '../../widgets/focusable_list_tile.dart';
 import '../../widgets/library_management_sheet.dart';
+import '../../widgets/overlay_sheet.dart';
 import '../../widgets/setting_tile.dart';
 import '../../widgets/settings_builder.dart';
 import '../../widgets/settings_section.dart';
@@ -159,6 +160,21 @@ class _SettingsScreenState extends State<SettingsScreen> with FocusableTab, Moun
   Widget build(BuildContext context) {
     final hasLibraries = context.select<LibrariesProvider, bool>((p) => p.libraries.isNotEmpty);
 
+    if (OverlaySheetController.maybeOf(context) != null) {
+      return _buildContent(context, hasLibraries: hasLibraries);
+    }
+
+    // Settings is hosted by MainScreen on side-navigation layouts, but it is a
+    // separate pushed route on phones. Add a route-local host only for the
+    // latter, and build its content from below the host so adaptive sheets do
+    // not fall back to modal routes with a competing Android back path.
+    return OverlaySheetHost(
+      canPop: true,
+      child: Builder(builder: (hostContext) => _buildContent(hostContext, hasLibraries: hasLibraries)),
+    );
+  }
+
+  Widget _buildContent(BuildContext sheetContext, {required bool hasLibraries}) {
     return Scaffold(
       body: Focus(
         onKeyEvent: _handleKeyEvent,
@@ -174,12 +190,12 @@ class _SettingsScreenState extends State<SettingsScreen> with FocusableTab, Moun
                     if (DonationService.isEnabled) _buildDonateTile(),
                     _buildAppearanceTile(),
                     _buildPlaybackTile(),
-                    if (hasLibraries) _buildManageLibrariesTile(),
+                    if (hasLibraries) _buildManageLibrariesTile(sheetContext),
                     _buildServicesTile(),
                   ],
                 ),
 
-                _buildConnectionsSection(),
+                _buildConnectionsSection(sheetContext),
 
                 if (!PlatformDetector.isAppleTV()) _buildDownloadsSection(),
 
@@ -258,7 +274,7 @@ class _SettingsScreenState extends State<SettingsScreen> with FocusableTab, Moun
     );
   }
 
-  Widget _buildManageLibrariesTile() {
+  Widget _buildManageLibrariesTile(BuildContext context) {
     return SettingNavigationTile(
       focusNode: _focusTracker.get(_kManageLibraries),
       icon: Symbols.video_library_rounded,
@@ -289,7 +305,7 @@ class _SettingsScreenState extends State<SettingsScreen> with FocusableTab, Moun
     );
   }
 
-  Widget _buildConnectionsSection() {
+  Widget _buildConnectionsSection(BuildContext context) {
     final active = context.select<ActiveProfileProvider, Profile?>((p) => p.active);
     final subtitle = active == null
         ? t.connections.addConnectionSubtitleNoProfile
@@ -311,12 +327,12 @@ class _SettingsScreenState extends State<SettingsScreen> with FocusableTab, Moun
             Navigator.push(context, MaterialPageRoute(builder: (_) => AddConnectionScreen(targetProfile: active)));
           },
         ),
-        _buildProfilesTile(),
+        _buildProfilesTile(context),
       ],
     );
   }
 
-  Widget _buildProfilesTile() {
+  Widget _buildProfilesTile(BuildContext context) {
     // ActiveProfileProvider already merges local rows with virtual Plex
     // Home profiles — counting only the local DB rows made every Plex Home
     // household read as a single profile here. `context.select` keeps

lib/widgets/library_management_sheet.dart

@@ -87,10 +87,9 @@ Future<void> showLibraryManagementSheet(
   if (PlatformDetector.isTV()) {
     return showScopedDialog<void>(context: context, builder: (context) => buildSheet(isDialog: true));
   }
-  // showAdaptive rather than of(context).show: on mobile, settings is a pushed
-  // route outside the OverlaySheetHost subtree, so only the fallback path is
-  // available there. isScrollControlled keeps the fallback modal from capping
-  // the sheet at ~9/16 of the screen.
+  // Use the host supplied by the calling screen when available while keeping
+  // this reusable entry point safe for routes without one. isScrollControlled
+  // keeps that modal fallback from capping the sheet at ~9/16 of the screen.
   return OverlaySheetController.showAdaptive<void>(
     context,
     showDragHandle: true,