fix: support missing/no-episodes library filters (API, UI, docs, tests)

src/server/api/anime.py

@@ -236,8 +236,8 @@ async def list_anime(
         sort_by: Optional sorting parameter. Allowed: title, id, name,
             missing_episodes
         filter: Optional filter parameter. Allowed values:
-            - "no_episodes": Show only series with no downloaded
-              episodes in folder
+            - "missing_episodes": Show only series that have any missing episodes
+            - "no_episodes": Show only series that have no downloaded episodes
         _auth: Ensures the caller is authenticated (value unused)
         anime_service: AnimeService instance provided via dependency
 
@@ -298,7 +298,7 @@ async def list_anime(
     # Validate filter parameter
     if filter:
         try:
-            allowed_filters = ["no_episodes"]
+            allowed_filters = ["missing_episodes", "no_episodes"]
             validate_filter_value(filter, allowed_filters)
         except ValueError as e:
             raise ValidationError(message=str(e))