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/soundtrack.sql

@@ -0,0 +1,49 @@
+-- name: ResetSoundtrackIdSeq :one
+SELECT setval('soundtrack_id_seq', (SELECT MAX(id) FROM soundtrack)+1);
+
+-- name: GetSoundtrackNameById :one
+SELECT soundtrack_name FROM soundtrack WHERE id = $1;
+
+-- name: GetSoundtrackById :one
+SELECT * 
+FROM soundtrack 
+WHERE id = $1 
+AND deleted IS NULL;
+
+-- name: SetSoundtrackDeletionDate :exec
+UPDATE soundtrack SET deleted=now() WHERE deleted IS NULL;
+
+-- name: ClearSoundtracks :exec
+DELETE FROM soundtrack;
+
+-- name: UpdateSoundtrackName :exec
+UPDATE soundtrack SET soundtrack_name=sqlc.arg(name), path=sqlc.arg(path), last_changed=now() WHERE id=sqlc.arg(id);
+
+-- name: UpdateSoundtrackHash :exec
+UPDATE soundtrack SET hash=sqlc.arg(hash), last_changed=now() WHERE id=sqlc.arg(id);
+
+-- name: RemoveSoundtrackDeletionDate :exec
+UPDATE soundtrack SET deleted=NULL WHERE id=$1;
+
+-- name: GetIdBySoundtrackName :one
+SELECT id FROM soundtrack WHERE soundtrack_name = $1;
+
+-- name: InsertSoundtrack :one
+INSERT INTO soundtrack (soundtrack_name, path, hash, added) VALUES ($1, $2, $3, now()) returning id;
+
+-- name: InsertSoundtrackWithExistingId :exec
+INSERT INTO soundtrack (id, soundtrack_name, path, hash, added) VALUES ($1, $2, $3, $4, now());
+
+-- name: FindAllSoundtracks :many
+SELECT *
+FROM soundtrack
+WHERE deleted IS NULL
+ORDER BY soundtrack_name;
+
+-- name: GetAllSoundtracksIncludingDeleted :many
+SELECT *
+FROM soundtrack
+ORDER BY soundtrack_name;
+
+-- name: AddSoundtrackPlayed :exec
+UPDATE soundtrack SET times_played = times_played + 1, last_played = now() WHERE id = $1;