Much too little time in my experience. Two weeks is just enough to start thinking that maybe not everything is shit, but not enough to really believe it. When you get back to work in this state of mind, you quickly realize that indeed, everything is shit, and you're much worse off than before.

1-2 weeks of vacation is what "normally" suffices, i.e., what "normal" people do. "Normal" people as contrasted with "burned out" or "on the road to burnout" people. It's not going to be enough for the latter group to do what is normally done: if it were enough, they wouldn't be burned out in the first place.

That just delays the inevitable, the OP has to deal with the root of the problem.