major refactor(game-modes): centralize scoring and turn handling

* Move common ball recording, scoring, and turn-switching logic into `BaseMode`
* Add hooks for mode-specific ball handling and turn behavior
* Simplify 8-ball and 9-ball modes to use `LastBallMode`
* Update Snooker to use the new ball-processing hooks
* Remove duplicated scoring and turn-management code

controllers/game/modes/game_manager_base.gd

@@ -21,5 +21,5 @@ func _balls_stopped_moving() -> void:
 	mode.handle_switch_user()
 
 func set_mode(game_mode) -> void:
-	mode            = Globals.game_data.GameMode.get(game_mode).new()
+	mode             = Globals.game_data.GameMode.get(game_mode).new()
 	mode.ball_states = mode.generate_ball_states()