I would say that I had no magic spider sense for fat adaption, the biggest change I noticed was while working out and or working in general. I did not need to stop, because of hunger at work, and my bike riding suffered(as does most cardio) then all of the sudden after really cutting back on the biking I could ride almost an unlimited amount after ignoring the limit I imposed. I felt no change in my weight training end, and the only other thing I noticed is that going up stairs did not kill me like it did when I was keto adapting.
I considered fat adaption started at 8 weeks, I considered myself fully fat adapted at around 25 weeks. Its not a light switch moment and it gets progressively better, things I did in the interim was to up my fat load that seemed make things go better.
I have seen people on these forums who were low carbish and super athletic in as little as 2-3 weeks, but that would be an outlier not a norm. Age, metabolic health, intake, strength of ketosis, level of carb intake, quality of diet, sleep, stress and sunlight all play into this.
You can be fat adapted and not be in ketosis, this is not a super big deal(If you over eat protien for instance). However if you have a high enough insluin spike fat adaption will not work much like ketosis shuts down, so you could suffer some. I would liken it to drinking alcohol. The recovery is much quicker, as little as hours for me now instead of days. I have not seen any studies or even research about it but from my understanding the process of fat adaption is more cellular health thing, because we eat so many carbs for so long the process more less decays to nearly useless(think of atrophy). Another thing that happens is that ketones production will go down once fat adaption kicks into full gear. This is why the pee sticks can become useless for some people as you are not making as many, your body is directly using the fat instead of it going to the liver, unlike when you are keto adapting you are relying on your liver for 100% of your energy via ketosis and GNG. I think if anything I lost some of the clarity when I fat adapted, and the more I fasted extended the lower the ketones have gotten on a normal non fasting basis. They still raise when fasting, but not to the levels there were. I Only measure acetone.
Keto adaption phase is being in ketosis and not being fat adapted. But you can only reach being fat adapted with ketones being high enough and insulin being low enough long enough. We are born in ketosis and some think fat adapted.