fix(sync): re-enrich live videos so ended streams gain duration

enrich_pending only touches enriched_at IS NULL, so a video first seen
while live was stamped live + duration-null and never revisited — staying
'live' with no duration forever after the broadcast ended. Add refresh_live
(run after each enrich pass) that re-fetches anything still live/upcoming,
plus just-ended was_live videos that haven't got their duration yet, until
they settle. Cheap: videos.list is 1 unit per 50 ids.

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 func, or_, select, update
+from sqlalchemy import and_, func, or_, select, update
 from sqlalchemy.dialects.postgresql import insert as pg_insert
 from sqlalchemy.orm import Session
 
@@ -260,6 +260,52 @@ def enrich_pending(db: Session, yt: YouTubeClient, limit: int | None = None) ->
     return enriched
 
 
+def refresh_live(db: Session, yt: YouTubeClient, limit: int | None = None) -> int:
+    """Re-fetch videos in a transient live state so they pick up their final shape.
+
+    `enrich_pending` is one-shot (it only touches enriched_at IS NULL), but a live broadcast
+    is not a final state: a stream ends and becomes a normal VOD — gaining a real duration
+    and flipping live_status to was_live — and an upcoming premiere eventually goes live then
+    ends. So we revisit anything still live/upcoming, plus a just-ended stream that hasn't got
+    its duration yet (YouTube can lag a bit after the broadcast), until it settles. Cheap:
+    videos.list is 1 unit per 50 ids, and the live/upcoming set is normally tiny."""
+    limit = limit or settings.enrich_batch_size
+    videos = (
+        db.execute(
+            select(Video)
+            .where(
+                or_(
+                    Video.live_status.in_(("live", "upcoming")),
+                    and_(
+                        Video.live_status == "was_live",
+                        Video.duration_seconds.is_(None),
+                    ),
+                )
+            )
+            .limit(limit)
+        )
+        .scalars()
+        .all()
+    )
+    if not videos:
+        return 0
+    items = {it["id"]: it for it in yt.get_videos([v.id for v in videos])}
+    now = _now()
+    updated = 0
+    for video in videos:
+        item = items.get(video.id)
+        if item is None:
+            # The broadcast vanished (deleted/private). Stop treating it as live so it
+            # doesn't get refreshed forever; it just becomes an ordinary (dead) row.
+            video.live_status = "none"
+            continue
+        apply_video_details(video, item)
+        video.enriched_at = now
+        updated += 1
+    db.commit()
+    return updated
+
+
 def run_shorts_classification(db: Session, limit: int | None = None) -> dict:
     """Finalize Shorts classification: cheaply mark non-candidates, then probe the
     youtube.com/shorts URL for short-enough, non-live, enriched videos."""