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/models.go

@@ -10,19 +10,6 @@ import (
 	"github.com/jackc/pgx/v5/pgtype"
 )
 
-type Game struct {
-	ID            int32      `json:"id"`
-	GameName      string     `json:"game_name"`
-	Added         time.Time  `json:"added"`
-	Deleted       *time.Time `json:"deleted"`
-	LastChanged   *time.Time `json:"last_changed"`
-	Path          string     `json:"path"`
-	TimesPlayed   int32      `json:"times_played"`
-	LastPlayed    *time.Time `json:"last_played"`
-	NumberOfSongs int32      `json:"number_of_songs"`
-	Hash          string     `json:"hash"`
-}
-
 type Session struct {
 	Token      string             `json:"token"`
 	IpAddress  string             `json:"ip_address"`
@@ -33,20 +20,33 @@ type Session struct {
 }
 
 type Song struct {
-	GameID      int32   `json:"game_id"`
-	SongName    string  `json:"song_name"`
-	Path        string  `json:"path"`
-	TimesPlayed int32   `json:"times_played"`
-	Hash        string  `json:"hash"`
-	FileName    *string `json:"file_name"`
+	SoundtrackID int32   `json:"soundtrack_id"`
+	SongName     string  `json:"song_name"`
+	Path         string  `json:"path"`
+	TimesPlayed  int32   `json:"times_played"`
+	Hash         string  `json:"hash"`
+	FileName     *string `json:"file_name"`
 }
 
 type SongList 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"`
+}
+
+type Soundtrack struct {
+	ID             int32      `json:"id"`
+	SoundtrackName string     `json:"soundtrack_name"`
+	Added          time.Time  `json:"added"`
+	Deleted        *time.Time `json:"deleted"`
+	LastChanged    *time.Time `json:"last_changed"`
+	Path           string     `json:"path"`
+	TimesPlayed    int32      `json:"times_played"`
+	LastPlayed     *time.Time `json:"last_played"`
+	NumberOfSongs  int32      `json:"number_of_songs"`
+	Hash           string     `json:"hash"`
 }
 
 type Vgmq struct {