Two things: there’s no such thing as full stack developer, and that’s definitely not the reason of the burnout.
I have already written in detail what full stack means in my opinion.
Burnout is a tricky thing; lots of psychologists tried to solve it, without much advancement. I think it’s simply when you loose interest in your job. You loose motivation. No reason to go on. So let’s switch careers.
Now if you truly are full stack, this will come much later. The fact you can do every type of job in a project means you won’t get bored for a while. Well, unless you have to do a lot of one specific type of task, which will eventually come in every project.
There’s a point when adding new features to a product is a bad idea. It works as intended, it brings in money, so you don’t have to touch it. There might be occasional bugfixes, there might be operational annoyances, but that product is essentially finished. That’s when most full stack devs will feel the burnout.
Also, during development, the main point is to add new features. It might be more diverse, but feature grinding can create lots of technical debt. That, again, can lead to the burnout feeling, as you have to work with the same pile of ugly code, which slowly becomes a burden.
I can probably go on with all the cases, but I will definitely not say “so you burn out because you are oble to do too many things.” Just find the balance between the tasks you like, and make tasks you don’t like enjoyable.
Happy coding!