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/repository/song_list.sql.go

@@ -11,7 +11,7 @@ import (
 )
 
 const getSongList = `-- name: GetSongList :many
-SELECT match_date, match_id, song_no, game_name, song_name
+SELECT match_date, match_id, song_no, soundtrack_name, song_name
 FROM song_list
 WHERE match_date = $1
 ORDER BY song_no DESC
@@ -30,7 +30,7 @@ func (q *Queries) GetSongList(ctx context.Context, matchDate time.Time) ([]SongL
 			&i.MatchDate,
 			&i.MatchID,
 			&i.SongNo,
-			&i.GameName,
+			&i.SoundtrackName,
 			&i.SongName,
 		); err != nil {
 			return nil, err
@@ -44,16 +44,16 @@ func (q *Queries) GetSongList(ctx context.Context, matchDate time.Time) ([]SongL
 }
 
 const insertSongInList = `-- 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)
 `
 
 type InsertSongInListParams struct {
-	MatchDate time.Time `json:"match_date"`
-	MatchID   int32     `json:"match_id"`
-	SongNo    int32     `json:"song_no"`
-	GameName  *string   `json:"game_name"`
-	SongName  *string   `json:"song_name"`
+	MatchDate      time.Time `json:"match_date"`
+	MatchID        int32     `json:"match_id"`
+	SongNo         int32     `json:"song_no"`
+	SoundtrackName *string   `json:"soundtrack_name"`
+	SongName       *string   `json:"song_name"`
 }
 
 func (q *Queries) InsertSongInList(ctx context.Context, arg InsertSongInListParams) error {
@@ -61,7 +61,7 @@ func (q *Queries) InsertSongInList(ctx context.Context, arg InsertSongInListPara
 		arg.MatchDate,
 		arg.MatchID,
 		arg.SongNo,
-		arg.GameName,
+		arg.SoundtrackName,
 		arg.SongName,
 	)
 	return err