Add splash screen functionality and update game state management

- Introduced GAME_SPLASH_SCREEN state in game.h
- Implemented splash_screen_init and splash_screen_update functions in splash_screen.c
- Updated game.c to initialize with GAME_SPLASH_SCREEN and handle splash screen updates
- Removed old splash screen code from main.c

include/game.h

@@ -28,6 +28,7 @@
 
 enum GameState
 {
+    GAME_SPLASH_SCREEN,
     GAME_MAIN_MENU,
     GAME_PLAYING,
     GAME_ROUND_END,
@@ -77,6 +78,7 @@ enum HandType
 // Game functions
 void game_init();
 void game_update();
+void game_set_state(enum GameState new_game_state);
 
 // Forward declaration
 struct List;