As somebody with social anxiety, it sounds like your MIL also has social anxiety. Hence, the constant need to have to reinforce that other people can stand her. I had to train this out of myself in my late teens/early 20s.
I know it’s annoying to deal with, but showing a little compassion and simply affirming that you’re exhausted but her relationship with you is secure will go a long way for her. She’ll probably get used to you being quiet around her too.
It’s just you trying to break out of the Matrix, but you keep waking up back inside it.