You are correct apparently that she did kill herself legally in Switzerland after a lifetime of treatment resistant depression, but she said the thing that really messed her up was treatment with SSRIs, not the stress of having been a man.
Although, she was hospitalized for a depressive breakdown during research for the book. She identified the reason as "the burden of deception," though, not specifically being treated as a man. From what I remember, she said that in a lot of ways being a man was actually less inherently stressful than being a woman (not having guys make eye contact with her, sort of play dominance games with her or try to interact with her, but just kind of let her go around and be left alone -- also that male friendships are more unconditionally supportive and friendly with each other than female). But yeah, I'm sure she couldn't fully "enjoy it" so to speak because of having to lead the double life full time or not feeling like she could really be friends with the people she was friends with.