Your body doesn't prefer glucose over fat. Too much glucose is toxic, so your body will focus on reducing it first. Too little is also dangerous so your body will make some from protein if necessary. But only as much as it needs.
Fat adaptation is about shifting your hormonal balance and response to retrain your body to maintain a lower level of glucose, and to retrain your cravings and hunger.
I'm not talking at the higher organism level, I'm talking at the very low-level chemistry in mitochondria. Glucose is "easier" to produce energy out of and so that happens preferentially from a chemistry perspective. Your body also needs a minimum level of glucose to survive.
When there isn't enough glycogen, the chemical balances in the mitochondria change and the liver mitochondria will produce glucose from whatever they have. This isn't a "decision" just the relative amounts of the chemicals change leading to one chemical pathway becoming more likely compared to another. This is all mediated by the random collisions of molecules in your cells. If you have a lot less of one molecule compared to another, the frequency that molecules find each other to do one thing v/s the other will change leading to different chemical pathways becoming more or less active.
There are many routes for your body to produce glucose. It is "easier" for your body to produce it from gluconegenic amino acids (not all amino acids can be used to produce glucose) than it is from fatty acids. It's the process of converting fatty acids into glucose that generates ketones. So when you have excess amino acids that can be turned into glucose, the chemistry will prefer this pathway over breaking down fat into glucose and this will lead to lower ketone production overall and kick you out of ketosis.
(I think I've gotten the gist of this right but any biochem experts feel free to correct me)
Fat adaptation is about shifting your hormonal balance and response to retrain your body to maintain a lower level of glucose, and to retrain your cravings and hunger.