I think you would be allowed to ask your academic advisor about writing a thesis when you have mental health considerations, I just am skeptical that an academic advisor is in a position to advise you helpfully. This one in particular sounds extremely skittish, overly so. Excessive fear of mental health considerations comes from unfamiliarity with them, and is not helpful.

My advice, as a general plan, is to confine discussions of mental health to those trained in such: mainly, counselors, social workers, psychiatrists, psychologists. So if you were still thinking about whether or not to write a thesis, your academic advisor and thesis advisor can help you on how long it might take, whether or not you have a good topic, how long it should be, etc. But they will not be able, in my opinion, to help you decide whether or not your mental health permits you to write a thesis.