Switching to the full game
Plan to start fresh in the full game. If you want to finish an in-progress Demo run, resume it in the Demo.
The quick answer
Slotbound Demo progress does not carry over to the full game. You can still save and resume an unfinished run within the Demo.
Steam Demo to full game
Plan to start fresh in the full game. If you want to finish an in-progress Demo run, resume it in the Demo.