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.sql

@@ -1,11 +1,11 @@
 -- name: ClearSongs :exec
 DELETE FROM song;
 
--- name: ClearSongsByGameId :exec
-DELETE FROM song WHERE game_id = $1;
+-- name: ClearSongsBySoundtrackId :exec
+DELETE FROM song WHERE soundtrack_id = $1;
 
 -- name: AddSong :exec
-INSERT INTO song(game_id, song_name, path, file_name, hash) VALUES ($1, $2, $3, $4, $5);
+INSERT INTO song(soundtrack_id, song_name, path, file_name, hash) VALUES ($1, $2, $3, $4, $5);
 
 -- name: CheckSong :one
 SELECT COUNT(*) FROM song WHERE path = $1;
@@ -22,14 +22,14 @@ UPDATE song SET song_name=$1, file_name=$2, path=$3 where hash=$4;
 -- name: AddHashToSong :exec
 UPDATE song SET hash=$1 where path=$2;
 
--- name: FindSongsFromGame :many
+-- name: FindSongsFromSoundtrack :many
 SELECT *
 FROM song
-WHERE game_id = $1;
+WHERE soundtrack_id = $1;
 
 -- name: AddSongPlayed :exec
 UPDATE song SET times_played = times_played + 1
-WHERE game_id = $1 AND song_name = $2;
+WHERE soundtrack_id = $1 AND song_name = $2;
 
 -- name: FetchAllSongs :many
 SELECT * FROM song;