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/models.py

@@ -203,6 +203,21 @@ class CollectionItem(Base):
     added_at = Column(DateTime, default=datetime.utcnow)
 
 
+class Playlist(Base):
+    __tablename__ = "playlists"
+
+    id = Column(Integer, primary_key=True, index=True)
+    youtube_playlist_id = Column(String, unique=True, nullable=False, index=True)
+    channel_id = Column(Integer, ForeignKey("channels.id", ondelete="CASCADE"), nullable=True)
+    title = Column(String, nullable=False)
+    description = Column(Text)
+    thumbnail_url = Column(String)
+    video_count = Column(Integer, default=0)
+    video_ids = Column(Text)  # JSON array of youtube_video_id strings
+    indexed_at = Column(DateTime)
+    crawled_at = Column(DateTime, default=datetime.utcnow)
+
+
 class GraphEdge(Base):
     __tablename__ = "graph_edges"
     __table_args__ = (UniqueConstraint("from_channel_id", "to_channel_id"),)