fix(libraries): add Plex TV date added sort

close #1369

lib/services/plex_client.dart

@@ -1791,16 +1791,18 @@ class PlexClient
   /// Append sort options that Plex honors via the `sort=` parameter but does not
   /// advertise in `/library/sections/{id}/sorts`.
   ///
-  /// Plays (`viewCount`) and the signed-in user's rating (`userRating`) both
-  /// sort correctly on movie/show libraries, so we surface them client-side
-  /// (mirroring how the Jellyfin sort list is built). De-duped by key so we
-  /// never double up if a future Plex version starts advertising them.
+  /// Date Added (`addedAt`), plays (`viewCount`), and the signed-in user's
+  /// rating (`userRating`) sort correctly on movie/show libraries, so we
+  /// surface them client-side (mirroring how the Jellyfin sort list is built).
+  /// De-duped by key so we never double up if a future Plex version starts
+  /// advertising them.
   List<MediaSort> _withExtraSorts(List<MediaSort> base, String? libraryType) {
     final type = libraryType?.toLowerCase();
     if (type != 'movie' && type != 'show') return base;
 
     final keys = base.map((s) => s.key).toSet();
     final extras = [
+      _dateAddedSort(),
       MediaSort(
         key: 'viewCount',
         descKey: 'viewCount:desc',
@@ -1818,18 +1820,22 @@ class PlexClient
     return [...base, ...extras];
   }
 
+  MediaSort _dateAddedSort() {
+    return MediaSort(
+      key: 'addedAt',
+      descKey: 'addedAt:desc',
+      title: t.libraries.sortLabels.dateAdded,
+      defaultDirection: 'desc',
+    );
+  }
+
   /// Build fallback sort options based on library type.
   ///
   /// If [libraryType] is null, returns generic sorts without the show-specific options.
   List<MediaSort> _getFallbackSorts(String? libraryType) {
     final fallbackSorts = <MediaSort>[
       MediaSort(key: 'titleSort', title: t.libraries.sortLabels.title, defaultDirection: 'asc'),
-      MediaSort(
-        key: 'addedAt',
-        descKey: 'addedAt:desc',
-        title: t.libraries.sortLabels.dateAdded,
-        defaultDirection: 'desc',
-      ),
+      _dateAddedSort(),
     ];
 
     // Add "Latest Episode Air Date" only for TV show libraries

test/services/plex_library_details_test.dart

@@ -77,7 +77,7 @@ void main() {
     ]);
   });
 
-  test('appends Plays and User Rating sorts only for movie/show libraries', () async {
+  test('appends Date Added, Plays, and User Rating sorts only for movie/show libraries', () async {
     PlexClient clientReturning() => makeClient((request) async {
       if (request.url.path == '/library/sections/1/sorts') {
         return http.Response(
@@ -99,7 +99,11 @@ void main() {
       final client = clientReturning();
       addTearDown(client.close);
       final sorts = await client.fetchSortOptions('1', libraryType: type);
-      expect(sorts.map((s) => s.key), ['titleSort', 'viewCount', 'userRating'], reason: type);
+      expect(sorts.map((s) => s.key), ['titleSort', 'addedAt', 'viewCount', 'userRating'], reason: type);
+
+      final dateAdded = sorts.singleWhere((s) => s.key == 'addedAt');
+      expect(dateAdded.descKey, 'addedAt:desc', reason: type);
+      expect(dateAdded.defaultDirection, 'desc', reason: type);
     }
 
     // Other library types (e.g. music) are left as the server returned them.
@@ -109,7 +113,7 @@ void main() {
     expect(musicSorts.map((s) => s.key), ['titleSort']);
   });
 
-  test('does not duplicate Plays/User Rating when the server already advertises them', () async {
+  test('does not duplicate Date Added/Plays when the server already advertises them', () async {
     final client = makeClient((request) async {
       if (request.url.path == '/library/sections/1/sorts') {
         return http.Response(
@@ -117,6 +121,7 @@ void main() {
             'MediaContainer': {
               'Directory': [
                 {'key': 'titleSort', 'title': 'Title', 'defaultDirection': 'asc'},
+                {'key': 'addedAt', 'title': 'Date Added', 'defaultDirection': 'desc'},
                 {'key': 'viewCount', 'title': 'Plays', 'defaultDirection': 'desc'},
               ],
             },
@@ -130,8 +135,8 @@ void main() {
     addTearDown(client.close);
 
     final sorts = await client.fetchSortOptions('1', libraryType: 'movie');
-    // viewCount already advertised -> not duplicated; userRating still appended.
-    expect(sorts.map((s) => s.key), ['titleSort', 'viewCount', 'userRating']);
+    // addedAt/viewCount already advertised -> not duplicated; userRating still appended.
+    expect(sorts.map((s) => s.key), ['titleSort', 'addedAt', 'viewCount', 'userRating']);
   });
 
   test('library content stamps known section when Plex omits librarySectionID on rows', () async {