The tills have keys to manually open them, and you can just record transactions on pen-and-paper if needed and enter them later. I've seen plenty of businesses do exactly that during power outages. Not as fast. But totally doable.

Stores with tills and freezers etc will have power for the tills but the backing network for payments probably won't be up. That's the concern with being cashless. They can accept cashxl, but no one has any.