For the new game and continue buttons, for sure, you can make them act however you want, you can find their events in Main menu scene → Buttons → New game and continue.
Currently, both buttons create TransitionToGame object and play it, and in New Game events you will see that if that transition has finished it change the scene to Game, You can easily change that by creating another shape painter object and name it what ever you want (Transition to New scene for example), then in new game events rather than creating and playing the TransitionToGame you create and paly the new shape painter object which will take you to the new scene you want (keep in mind the New Game button will also delete your data and make you start the game from 0, if you don't want that then you can remove the Delete storage action from the event).
As for the rework, it looks amazing great job ! 💪