How the manager responds to you having a burnout, however, is what’s important. A good manager will manage to accelerate your recovery, and come up with some plan to prevent it from happening again in the future.
I also believe that in the end, stress management is something that in the end, it’s best you take your own responsibility for. Learn to say no, learn to communicate about your limits, and learn to walk away / push back in case those limits are crossed.
I went through a few burn outs through various phases of my life, and almost always it was a combination of multiple things at once. While a manager can help, in the end I am responsible for my own mental well being.