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/migrations/000005_rename_game_to_soundtrack.down.sql

@@ -0,0 +1,33 @@
+-- Revert: Rename soundtrack table back to game
+ALTER TABLE soundtrack RENAME TO game;
+
+-- Revert primary key sequence
+ALTER SEQUENCE soundtrack_id_seq RENAME TO game_id_seq;
+
+-- Revert columns in game table
+ALTER TABLE game RENAME COLUMN soundtrack_name TO game_name;
+
+-- Revert song table: rename soundtrack_id back to game_id
+ALTER TABLE song RENAME COLUMN soundtrack_id TO game_id;
+
+-- Revert song primary key
+ALTER TABLE song DROP CONSTRAINT IF EXISTS song_pkey;
+ALTER TABLE song ADD PRIMARY KEY (game_id, path);
+ALTER TABLE song RENAME CONSTRAINT song_pkey_soundtrack TO song_pkey;
+
+-- Revert song_list table references
+ALTER TABLE song_list RENAME COLUMN soundtrack_name TO game_name;
+
+-- Revert foreign key constraint
+ALTER TABLE song DROP CONSTRAINT IF EXISTS song_soundtrack_id_fkey;
+ALTER TABLE song ADD CONSTRAINT song_game_id_fkey 
+    FOREIGN KEY (game_id) REFERENCES game(id);
+
+-- Revert indexes
+ALTER INDEX IF EXISTS idx_soundtrack_deleted RENAME TO idx_game_deleted;
+ALTER INDEX IF EXISTS idx_soundtrack_hash RENAME TO idx_game_hash;
+ALTER INDEX IF EXISTS idx_soundtrack_path RENAME TO idx_game_path;
+ALTER INDEX IF EXISTS idx_soundtrack_name RENAME TO idx_game_name;
+ALTER INDEX IF EXISTS idx_song_soundtrack_id RENAME TO idx_song_game_id;
+ALTER INDEX IF EXISTS idx_song_soundtrack_id_song_name RENAME TO idx_song_game_id_song_name;
+ALTER INDEX IF EXISTS song_list_soundtrack_name_idx RENAME TO song_list_game_name_idx;

internal/db/migrations/000005_rename_game_to_soundtrack.up.sql

@@ -0,0 +1,33 @@
+-- Rename game table to soundtrack
+ALTER TABLE game RENAME TO soundtrack;
+
+-- Rename primary key sequence
+ALTER SEQUENCE game_id_seq RENAME TO soundtrack_id_seq;
+
+-- Rename columns in soundtrack table
+ALTER TABLE soundtrack RENAME COLUMN game_name TO soundtrack_name;
+
+-- Update song table: rename game_id to soundtrack_id
+ALTER TABLE song RENAME COLUMN game_id TO soundtrack_id;
+
+-- Update song primary key
+ALTER TABLE song DROP CONSTRAINT IF EXISTS song_pkey;
+ALTER TABLE song ADD PRIMARY KEY (soundtrack_id, path);
+ALTER TABLE song RENAME CONSTRAINT song_pkey TO song_pkey_soundtrack;
+
+-- Update song_list table references
+ALTER TABLE song_list RENAME COLUMN game_name TO soundtrack_name;
+
+-- Rename foreign key constraint
+ALTER TABLE song DROP CONSTRAINT IF EXISTS song_game_id_fkey;
+ALTER TABLE song ADD CONSTRAINT song_soundtrack_id_fkey 
+    FOREIGN KEY (soundtrack_id) REFERENCES soundtrack(id);
+
+-- Rename indexes
+ALTER INDEX IF EXISTS idx_game_deleted RENAME TO idx_soundtrack_deleted;
+ALTER INDEX IF EXISTS idx_game_hash RENAME TO idx_soundtrack_hash;
+ALTER INDEX IF EXISTS idx_game_path RENAME TO idx_soundtrack_path;
+ALTER INDEX IF EXISTS idx_game_name RENAME TO idx_soundtrack_name;
+ALTER INDEX IF EXISTS idx_song_game_id RENAME TO idx_song_soundtrack_id;
+ALTER INDEX IF EXISTS idx_song_game_id_song_name RENAME TO idx_song_soundtrack_id_song_name;
+ALTER INDEX IF EXISTS song_list_game_name_idx RENAME TO song_list_soundtrack_name_idx;