Realistically I wanna say that your last paragraph sounds perfectly worded to broach the topic with her.

It tells her that you do not fundamentally want to isolate her, that she should be able to talk about stuff with friends but that you want some things to be private or at least have a say on how or if something gets discussed with friends.

Maybe try to frame what the deciding factor is to make something private for you as well?

I do not feel comfortable if you air out our discussions on weaknesses when those are moments where I feel we can be vulnerable and frank with each other. I just do not want to feel like I share those critical moments with all our friends and family but I want to at least have time to digest it myself. If we improve and/or it feels like we have progressed from the topic I think it is fair game but otherwise it really puts pressure on me.

Maybe something like this, if it fits what you are feeling?

But I think discussing it is the right way forward and I know how hard it can be to talk with a partner about stuff like this.