fix: refine game mode state tracking and turn handling

* Centralize ball state generation in `BaseMode`
* Track turn count, player, and ball state consistently
* Prevent 8-ball, 9-ball, and colored snooker balls from being marked valid when reaped/sunk
* Update mode initialization and ball-state assignment
* Normalize Free Ball mode node name to `freeball`

controllers/game/modes/free_ball.gd

@@ -1,6 +1,9 @@
 class_name FreeBall extends BaseMode
 
 
+func  _init() -> void:
+	pass
+
 func reap_ball(ball: Node3D) -> void:
 	super(ball)
 
@@ -17,9 +20,11 @@ func handle_switch_user() -> void:
 
 	if balls_sunk.is_empty():
 		Globals.game_state.switch_active_player()
+		turn_count += 1
 		return
 
 	# TODO: Handle points, etc
 	# Globals.multiplayer_data.current_turn_player_id
 
 	balls_sunk.clear()
+	turn_count += 1