I do intermittent fasting.
My breath stinks quite a bit on days I don't eat. The bacteria develop very well on those days, since they're not being washed off as often. And that's before "keto breath" even comes into play.
Point is, your mouth bacteria are fine producing all sorts of "charming" smells even without food.
You probably do stink. The two of you are just used to it.
https://youtu.be/bQcL0t73O5Y?si=xQmT9EZtVwWqQOas