I never thought about it too deeply, but now that I think about it a little bit more deeply, but still not that deep anyways, the process we're talking about doesn't really sound like an adaptation so much. Instead, I prefer to see it as declogging the carburator.

Insulin regulates fat tissue. The more insulin, the less fuel comes out. Go low-carb, insulin drops, fuel starts pouring out. While it's likely that some systems need to rev back up at this point, it's not like they have to adapt to something they've never done before, it's just that they haven't done it that much for a while now.

As the liver produces more ketones, there's CMA going on, and this means literal declogging of the blood and inside the cells as glycated proteins get broken up and their elements used for something at last. We see this as a drop of HbA1c for example. Anyways, as this is going on, the systems that rely on these proteins - enzymes and hormones and lipoproteins and so forth - rev up as well.

A few days or weeks later, the various systems now work more than they used to, but not more than normal - they are working normally now because they are no longer disrupted by a constant influx of dietary carbs and subsequent hyperinsulinemia.

So, fat adapted? Sure, let's keep the term so we know what we're talking about, but it doesn't actually mean adaptation in my view.