fix(sync): an empty answer the remote's own count contradicts is not believed, one level down

E32 review round 1 (B1, B2, B3, B8).

- Plex watch reconcile: a section the server SAYS is empty (totalSize 0, nothing listed) is a
  complete listing. It read as "cut short" forever, so one empty library stopped un-watches from
  ever syncing. A listing with no total at all stays incomplete (the client now returns None for
  it instead of 0), and a whole scan that listed nothing still clears nothing. Tests now cover
  completeness across two sections, both orders.
- Plex collections: no members from a collection whose listing counts some (childCount) keeps
  the membership we hold, in the full sync and in the targeted resync after a write.
- YouTube playlists: no items for a playlist whose listing counts some (itemCount) keeps the
  mirror in the bulk pull, and is refused as retryable in "reset to YouTube" and in the push
  plan/merge, where it read as "YouTube deleted them all". The rule sits beside vanished().
- A playlist deleted on YouTube answered "reconnect your account"; it now says it is gone
  (errors.youtube.gone, HU+EN).
- The pure 3-way merge moved to sync/playlist_merge.py; playlists.py is back under 800 lines and
  off the size list.

backend/app/youtube/client.py

@@ -114,7 +114,7 @@ _DEAD_GRANT = "invalid_grant"
 
 # What a refused YouTube action means to the person who asked for it — the three things they can
 # act on differently: wait for tomorrow's budget, reconnect the account, or try again later.
-YouTubeRefusal = Literal["quota", "reconnect", "unavailable"]
+YouTubeRefusal = Literal["quota", "reconnect", "unavailable", "gone"]
 
 
 def refusal_reason(exc: YouTubeError) -> YouTubeRefusal:
@@ -126,6 +126,9 @@ def refusal_reason(exc: YouTubeError) -> YouTubeRefusal:
     the account would still read as connected, with no connect button to press."""
     if is_quota_refusal(exc):
         return "quota"
+    if exc.reason == "playlistNotFound":
+        # The list itself is gone (deleted on YouTube): neither a retry nor a reconnect helps.
+        return "gone"
     if exc.path == "oauth2/token":
         return "reconnect" if exc.reason == _DEAD_GRANT else "unavailable"
     if not exc.path and exc.reason != "transport":
@@ -423,16 +426,22 @@ class YouTubeClient:
         return resp.json() if resp.content else {}
 
     def get_playlist_snippet(self, playlist_id: str) -> dict | None:
-        """The snippet (title/description) of one playlist, or None if it no longer
-        exists. 1 unit (OAuth, so private playlists work)."""
+        """The snippet (title/description) of one playlist plus its `item_count` (what an empty
+        item listing is checked against), or None if it no longer exists. 1 unit (OAuth, so
+        private playlists work)."""
         data = self._get(
             "playlists",
-            {"part": "snippet", "id": playlist_id, "maxResults": 1},
+            {"part": "snippet,contentDetails", "id": playlist_id, "maxResults": 1},
             cost=1,
             allow_key=False,
         )
         items = data.get("items", [])
-        return items[0].get("snippet") if items else None
+        if not items:
+            return None
+        return {
+            **(items[0].get("snippet") or {}),
+            "item_count": items[0].get("contentDetails", {}).get("itemCount"),
+        }
 
     def update_playlist_title(self, playlist_id: str, title: str) -> None:
         """Rename a playlist on YouTube. 50 units."""