I have found that in trying to deal with ptsd, I have been left on the equivalent of "truth serum".
I would ask myself, "Who needs to know? To what extent is it their business, and how many details are they required to know?"
You are not being dishonest to say you are off work, or that it is "work-related", IMHO.
Personally, knowing what I know, seeing how others react, I wouldn't tell anyone more than the bare minimum, and only if that was necessary.
When I am asked a question that is too personal, sometimes I ask the other person something very personal about their business. That seems to end that line of questioning.
Or I say, "I give up, why am I (off work, etc)?", lol
Do what feels right to you. You know who you can trust better than anyone else.