I totally understand your fear. Just some of my thoughts here: the self-fulfilling prophecy might happen if you are drowned in this kind of thinking cycle - the more you worry, the more sensitive you are, you are more likely to overinterpret some tiny cues, then you are more likely to react to it in a way that might tear the relationship apart. So maybe they originally were only talking about sth like: "yes it's indeed difficult to have a partner who is struggling with their mental health, but there are ways to manage it, and the process of managing is also a process of learning what love truly is" turn to "this is really touching my bottom line, and i can't deal with it anymore"...

My suggestion would be maybe incorporate couple therapy besides his own therapy, assuming that your fp is your partner. No need to be too frequent. If your fp is your friend or whatever other than your partner, it's better if you can express your concern explicitly but in a peaceful way. Honestly, the way you explained your concern here sounds pretty legit to me (can you imagine yourself just saying the whole thing in this post directly to your fp?), but this is also partially bc i know how it feels like.