Mine is also toothless by now. You are correct, my vet told my they're using their upper denture / jaw to crush what needs to be crushed and swallow everything else.

I was told to be careful with wet food and meat because this kind of stuff can't be crushed so it should be "bite sized" to allow her to swallow her food easily. But I don't know if this is a general thing or if this was related to an incident when my cat nearly suffocated from a piece of sausage she greedily swallowed without chewing... She's never been the sharpest tool in the shed, but we love her (⁠人⁠ ⁠•͈⁠ᴗ⁠•͈⁠)