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.

1 files changed, 6 insertions, 0 deletions

diff --git a/Emby.Server.Implementations/Library/LibraryManager.cs b/Emby.Server.Implementations/Library/LibraryManager.cs
index 19371f68d7..9bb962c504 100644
--- a/Emby.Server.Implementations/Library/LibraryManager.cs
+++ b/Emby.Server.Implementations/Library/LibraryManager.cs
@@ -2235,6 +2235,12 @@ namespace Emby.Server.Implementations.Library
         }
 
         /// <inheritdoc />
+        public IReadOnlySet<Guid> GetItemsWithAlternateVersions(IReadOnlyList<Guid> itemIds)
+        {
+            return _linkedChildrenService.GetItemsWithAlternateVersions(itemIds);
+        }
+
+        /// <inheritdoc />
         public void UpsertLinkedChild(Guid parentId, Guid childId, MediaBrowser.Controller.Entities.LinkedChildType childType)
         {
             _linkedChildrenService.UpsertLinkedChild(parentId, childId, childType);