I burnt my self out a few years back after spending 3 years working full-time on a startup. Since then I've been working for a FAANG.
One thing I've never really recovered is the passion I had for side projects. Worse than that, I can't actually think of anything worth building, or even tinkering with, which is sad, as spending some of my free time on side projects was something I really enjoyed.
If you've found yourself in a similar position, how have you dealt with it?
I know how this feels. After a few bouts of burnout over my ~20 year career, I'm not convinced we fully recover from all of it. I think each bout leaves some permanent damage, along with increased risk of subsequent bouts. I made a similar comment here: https://news.ycombinator.com/item?id=22164678
The best general advice I can give is don't push anything. If you're not feeling motivated to engage in a side project, no problem, don't pursue one right now. Give things time and see how you feel after 2-6 months. Other general advice - reduce work hours if you can, exercise regularly, and relax. Morning/evening walks combine the latter two well.
Learning something new can also help combat burnout fogginess. I've found courses in something of interest work well (search Coursera, Udacity, Udemy, etc.). What I like about these is they're smaller in scale and more self contained than an open-ended side project. They allow you to commit time and energy in small chunks and at your own pace, but still leave you with something valuable in the end. E.g. over the years I've taken courses in Vue, Svelte, TypeScript, and a couple math refreshers. All enjoyable and worth while IMO.