feat: Rename game to soundtrack throughout codebase

- Database migration: rename game table to soundtrack
- Rename game_name to soundtrack_name, game_id to soundtrack_id
- Update all SQL queries in soundtrack.sql, song.sql, song_list.sql, statistics.sql
- Regenerate sqlc code (soundtrack.sql.go, song.sql.go, etc.)
- Update backend: music.go, sync.go, statistics.go
- Update server: musicHandler.go, syncHandler.go, routes.go
- Update frontend: hello.go
- Keep URL paths as /games for backward compatibility

Generated by Mistral Vibe.
Co-Authored-By: Mistral Vibe <vibe@mistral.ai>

internal/db/queries/song_list.sql

@@ -1,5 +1,5 @@
 -- name: InsertSongInList :exec
-INSERT INTO song_list (match_date, match_id, song_no, game_name, song_name)
+INSERT INTO song_list (match_date, match_id, song_no, soundtrack_name, song_name)
 VALUES ($1, $2, $3, $4, $5);
 
 -- name: GetSongList :many