I don’t think the body becomes more efficient at utilising the energy stores, it’s more a case of your muscles working more efficiently when you get more trained. By that I mean you stop doing unneccessary movements, for example a beginner might grip the bars very tightly, which needs energy for his arm muscles, while later on you can stay more relaxed. Also I’d think on a smalller scale muscle bundles develop a more synchronised firing pattern that fits the movement better, etc. However none of that affects your energy needs for other functions, eg to keep warm, supply the brain, or other organs. There might be a slight increase in efficiency of the heart and lungs, eg lower HR at rest, but I can’t see that making a big difference in resting matabolism.
If anything, if you have increased muscle mass and less fat to keep you warm, you’ll likely burn more calories, even at rest.