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/database.py

@@ -84,6 +84,7 @@ def init_db():
     try:
         # Column migrations — safe to run on every startup
         _add_column_if_missing(raw_conn, "videos", "view_count", "INTEGER")
+        _add_column_if_missing(raw_conn, "videos", "like_count", "INTEGER")
         raw_conn.commit()
         # executescript handles multi-statement SQL including trigger BEGIN...END blocks
         raw_conn.executescript(FTS_SETUP_SQL)