Your body is always burning fat, it's not a state machine, it's a super parallel bunch of cells. The proportion varies robustly with energy demand, oxygen supply is the limiting factor to meeting the demand and getting fat into energy is less oxygen efficient than doing the same with glycogen.

But this is an entirely academic point designed to mislead people. Given glycogen stores top out at ~8 MJ while there is many many magnitudes more in fat, it's like delving into the details of L2 cache or main memory. It's down in the noise given weight gain or loss is a months long process.

Hey, if you feel like you can better maintain by trying to be permanently glycogen depleted, you do you. But why that works or doesn't really has nothing to do with any of the things you mentioned.