Add like count to videos

Same pattern as view_count: model column, yt-dlp extraction, SQL select,
VideoDetail field, startup migration, and display in Watch meta row.

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

backend/services/ytdlp.py

@@ -75,6 +75,7 @@ def _normalize_video(info: dict) -> dict:
         "category": info.get("category") or (info.get("categories") or [None])[0],
         "chapters": json.dumps(chapters) if chapters else None,
         "view_count": info.get("view_count"),
+        "like_count": info.get("like_count"),
         "channel": {
             "youtube_channel_id": info.get("channel_id"),
             "name": info.get("channel") or info.get("uploader", ""),