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.