Batch alternate version detection in DtoService to remove MediaSourceCount N+1

Browsing a page of videos with the MediaSourceCount field ran one alternate
version query per item, each opening a fresh DbContext. On a large library that
turned a single page into hundreds of sequential round trips and made the Items
endpoint take tens of seconds while holding a request thread the whole time.

Detect which videos own alternate versions once per page with a single query,
mirroring the existing people batch. Videos absent from that set have a single
media source, so the per item lookups are skipped for the common case. Behavior
is unchanged: a video with no alternates already resolved to a count of one.

Adds a regression test asserting the count resolves from the batch and the per
item lookups are never called.

MediaBrowser.Controller/Library/ILibraryManager.cs

@@ -255,6 +255,14 @@ namespace MediaBrowser.Controller.Library
         /// <returns>Enumerable of linked Video items.</returns>
         IEnumerable<Video> GetLinkedAlternateVersions(Video video);
 
+        /// <summary>
+        /// Gets, in a single query, the subset of the supplied items that own at least one alternate
+        /// version (local or linked). Items absent from the result have no alternate versions.
+        /// </summary>
+        /// <param name="itemIds">The item IDs to check.</param>
+        /// <returns>The set of item IDs that have alternate versions.</returns>
+        IReadOnlySet<Guid> GetItemsWithAlternateVersions(IReadOnlyList<Guid> itemIds);
+
         /// <summary>
         /// Creates or updates a LinkedChild entry linking a parent to a child item.
         /// </summary>

MediaBrowser.Controller/Persistence/ILinkedChildrenService.cs

@@ -19,6 +19,15 @@ public interface ILinkedChildrenService
     /// <returns>List of child item IDs.</returns>
     IReadOnlyList<Guid> GetLinkedChildrenIds(Guid parentId, int? childType = null);
 
+    /// <summary>
+    /// Gets, in a single query, the subset of the supplied items that own at least one alternate
+    /// version (local or linked). Items absent from the result have no alternate versions, so their
+    /// media source count is one.
+    /// </summary>
+    /// <param name="itemIds">The item IDs to check.</param>
+    /// <returns>The set of item IDs that have alternate versions.</returns>
+    IReadOnlySet<Guid> GetItemsWithAlternateVersions(IReadOnlyList<Guid> itemIds);
+
     /// <summary>
     /// Gets all artist matches from the database.
     /// </summary>