Speaking from personal experience, when I was deeply fatigued during my PhD (due to overwork), I spent two weeks of vacation doing nothing and felt as exhausted on the last day of my vacation. It just took longer to recover, and I set some personal boundaries then that have served me well. But if your fatigue is really deep, you might need much more time.
This is a huge struggle for me, and I can empathize. Some factors are external, some internal. When something weighs heavily on my mind, I have trouble sleeping sometimes. Sometimes when I pee at night (one way nature reminds me I have reached middle age), I have trouble getting back to sleep again.
Other times our kids wake me up. On Tuesday, our daughter pooped her pants and I had to take a shower at 4:30 am. Fortunately, it was 4:30 already, my alarm was set for 4:45 … Other times, I am not so lucky.
I don’t think there is any simple advice to give you, but two things have helped me: I really made an effort over several years to improve my sleep. And second, if I haven’t slept more than 7–7:30 hours, I don’t train. Since I love to train, this gives me motivation to fix my sleep.
I would take how you feel over the opinion of any app. If you feel exhausted and without energy, then that’s that.
Maybe I’m overstepping your boundaries, but does depression run in your family? Is work of family really stressing you out? You shouldn’t need a bike ride to allow you to sleep.
Personally, my time on the bike is part of my self care (self therapy in a sense), if I don’t do sports for a long period, I get cranky and restless. However, if sports is contributing to your lack of motivation and lack of energy, you might want to keep it easy. I don’t know if we here can help you with any of that, but don’t give up and be kind to yourself.