fix(backfill): auto-complete full history when stored >= video_count

A channel whose stored uploads already meet or exceed YouTube's advertised
video_count holds its whole history, but backfill_done could stay false forever
when the deep cursor never reached the end (e.g. a small channel that was never
deep-requested, so the demand-driven deep job never ran). Such channels nagged
as 'needs full history' despite having every video. Add reconcile_full_history()
(idempotent, no quota) and run it at the end of each recent/deep backfill cycle
so backfill_done self-heals.

backend/app/sync/videos.py

@@ -5,7 +5,7 @@ import re
 from concurrent.futures import ThreadPoolExecutor
 from datetime import datetime, timedelta, timezone
 
-from sqlalchemy import or_, select, update
+from sqlalchemy import func, or_, select, update
 from sqlalchemy.dialects.postgresql import insert as pg_insert
 from sqlalchemy.orm import Session
 
@@ -173,6 +173,32 @@ def backfill_channel_deep(
     return total
 
 
+def reconcile_full_history(db: Session) -> int:
+    """Mark channels fully backfilled once their stored uploads meet or exceed YouTube's
+    advertised video_count. The uploads playlist length is normally <= the advertised
+    count, so 'stored >= video_count' means we already hold the whole history — even if
+    the deep cursor never reached the end (e.g. a small channel that was never
+    deep-requested, so the demand-driven deep job never ran). Without this such a channel
+    sits in 'needs full history' forever despite having every video. Idempotent, no API
+    quota; returns the number of channels flipped."""
+    stored = (
+        select(func.count(Video.id))
+        .where(Video.channel_id == Channel.id)
+        .scalar_subquery()
+    )
+    result = db.execute(
+        update(Channel)
+        .where(
+            Channel.backfill_done.is_(False),
+            Channel.video_count.is_not(None),
+            stored >= Channel.video_count,
+        )
+        .values(backfill_done=True, backfill_cursor=None)
+    )
+    db.commit()
+    return result.rowcount
+
+
 # --- Enrichment (videos.list) ---
 def _live_status(snippet: dict, live_details: dict | None) -> str:
     broadcast = snippet.get("liveBroadcastContent")