The problem is that after an extended period of high-carbohydrate, low-fat eating, the mitochondria get damaged enough from the reactive oxygen species generated by glucose metabolism that they no longer function properly. Certain other cellular processes shut down from lack of use. The fat-adaptation period involves both the healing of mitochondria, the birth of new mitochondria, and the reactivation of those shut-down cellular processes. So yes, fat-adaptation is indeed the regaining of the ability to metabolise fatty acids.
The muscle weakness comes from the fact that the muscular mitochondria are not active enough to metabolise fatty acids, they can barely manage ketones, and the muscles’ supply of glucose has been greatly reduced. As the mitochondria heal, as new mitochondria are created, and as the other necessary metabolic pathways in the cells are reactivated, the person regains strength and endurance. Many people find that after the adaptation period is over, their endurance is actually better than it ever was.
Explosive performance takes longer to recover. No one seems to know quite how much longer, but we do know that in endurance athletes who have been eating a ketogenic diet for at least two years, their glycogen levels are indistinguishable from those of carb-adapted athletes. So glycogen levels recover somewhere between a minimum of eight weeks to sometime less than 24 months.