Add playlists support and fix explore older videos

- New playlists router: fetch channel playlists from YouTube, index
  playlist videos, browse by playlist with pagination
- Playlist model gets video_ids column to store ordered video list
- Register playlists router in main.py with DB migration
- Add Playlists tab to Channel page: grid of playlist cards, click to
  browse videos, index/re-index per playlist
- Fix explore older videos skipping all entries without published_at;
  flat-playlist entries for older videos rarely include timestamp data

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/routers/channels.py

@@ -858,7 +858,7 @@ def _index_channel_explore_task(channel_id: int, user_id: int, start_video: int,
             return
         for vdata in result.get("videos", []):
             yt_id = vdata.get("youtube_video_id")
-            if not yt_id or not vdata.get("published_at"):
+            if not yt_id:
                 continue
             if not db.query(Video).filter_by(youtube_video_id=yt_id).first():
                 db.add(Video(