With Simmons, I don't think it is either/or, black or white that mental health issues are the entire issue or not. Simmons is a bit of a head case. Missing FTs for example is mostly in his head. But does that qualify as a mental health issue? Probably not.
I suspect that Simmons would not meet the clinical threshold of having a psychological illness to the level that would prevent him from playing if he wanted to play. But that does not mean he is 100% mentally fit either. It is like a physical injury when they say someone is hurt but not injured. It is not always 100% clear what the line is between injured, shouldn't play, vs. hurt, can play through it. And this line changes whether it is the playoffs or just game 44 of the regular season and game 2 of a back to back. I suspect that this applies to mental fitness also.
Even though I believe that Simmons could play if he wanted to, I do also believe that he is messed up or not 100% mentally fit or whatever colloquial term you want to use. Any team that trades for him is going to have to do some work to get him ready to play both mentally and physically. If the new team ignores the mental part, I doubt they get the most out of him.