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/models.py

@@ -61,6 +61,7 @@ class Video(Base):
     category = Column(String)
     chapters = Column(Text)  # JSON array of {start_time, end_time, title}
     view_count = Column(Integer)
+    like_count = Column(Integer)
 
 
 class UserVideo(Base):