Saving should work whenever the activity menu is up, What do you mean it's broken?
More interactivity will come, mini-games are in development. Skim subscrbestar or patreon for details.
Its not just hitting the skip button that disables the save function, its also when you press the progression button at all. I've attempted two playthroughs, both get stuck after act 2. Admittedly it makes the game unplayable.
The latest update (L) fixes the issue in Act 3.
Saving should work in the evening, whenever you see the "do nothing" button or other buttons.
