Do I stay on PIP even though my mental health will suffer?

Hello, I am looking for some advice. Everything was great at my job and my performance was excellent until all of a sudden they started nitpicking me. I was given a written warning and now a 30day PIP. The conditions of the pip are kind of awful, my boss is attached to my hip, will be attending every meeting I have, needs a copy of every email, and we are meeting daily to discuss performance. It’s clear to me they want to push me out. The last two weeks since they started nitpicking, have been so hard and stressful and I am not sleeping at night. My self esteem is in the gutter and I'm defeated and unmotivated. I don't know if I can last another 30 days.

So my dilemma- do I quit and give myself a breather, or do I continue to suffer and collect unemployment when they fire me?

I have some money saved up and I am already applying to jobs, but it could be months until I find another job.