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/server/musicHandler.go

@@ -229,8 +229,8 @@ func (m *MusicHandler) GetPreviousSong(ctx *echo.Context) error {
 	return ctx.Stream(http.StatusOK, "audio/mpeg", file)
 }
 
-// GetAllGames godoc
-// @Summary Get all games
+// GetAllSoundtracks godoc
+// @Summary Get all soundtracks
 // @Description Returns a list of all games in order
 // @Tags music
 // @Accept json
@@ -238,17 +238,17 @@ func (m *MusicHandler) GetPreviousSong(ctx *echo.Context) error {
 // @Success 200 {array} map[string]interface{}
 // @Failure 423 {string} string "Syncing is in progress"
 // @Router /music/all/order [get]
-func (m *MusicHandler) GetAllGames(ctx *echo.Context) error {
+func (m *MusicHandler) GetAllSoundtracks(ctx *echo.Context) error {
 	if backend.Syncing {
 		logging.GetLogger().Info("Syncing is in progress")
 		return ctx.JSON(http.StatusLocked, "Syncing is in progress")
 	}
-	gameList := backend.GetAllGames()
-	return ctx.JSON(http.StatusOK, gameList)
+	soundtrackList := backend.GetAllSoundtracks()
+	return ctx.JSON(http.StatusOK, soundtrackList)
 }
 
-// GetAllGamesRandom godoc
-// @Summary Get all games random
+// GetAllSoundtracksRandom godoc
+// @Summary Get all soundtracks random
 // @Description Returns a list of all games in random order
 // @Tags music
 // @Accept json
@@ -256,13 +256,13 @@ func (m *MusicHandler) GetAllGames(ctx *echo.Context) error {
 // @Success 200 {array} map[string]interface{}
 // @Failure 423 {string} string "Syncing is in progress"
 // @Router /music/all/random [get]
-func (m *MusicHandler) GetAllGamesRandom(ctx *echo.Context) error {
+func (m *MusicHandler) GetAllSoundtracksRandom(ctx *echo.Context) error {
 	if backend.Syncing {
 		logging.GetLogger().Info("Syncing is in progress")
 		return ctx.JSON(http.StatusLocked, "Syncing is in progress")
 	}
-	gameList := backend.GetAllGamesRandom()
-	return ctx.JSON(http.StatusOK, gameList)
+	soundtrackList := backend.GetAllSoundtracksRandom()
+	return ctx.JSON(http.StatusOK, soundtrackList)
 }
 
 // PutPlayed godoc