HR Manager putting a copy of PIP under my door and open

A department that pips you is not one you want to stay in, especially handled as poorly as this. I suggest you start looking for new employment.

That said, I fought a pip and won years ago, but as another commenter stated, it damaged all ability to get promoted and I was Punished for overcoming in a variety of other more subtle ways. I think I put up with it from my crappy past, I've healed a lot since then. In my case it was clear that the ethos of management by pip came from the head of the dept even tho that person was not directly involved. My winning made her look bad by showing the absurdity of that approach. In hindsight I wish I'd left sooner. But I had young kids and was primary wage earner. If your company is large, it can still be beneficial to move to an unrelated dept to get out of that situation.

If the PIP is inaccurate, what is their goal? As a woman, you're in a protected class in the US. Is this happening to others? Definitely see a lawyer or HR/exit strategist for a professional perspective and look for patterns of behavior or perceptions that may have led to this. If someone slipped a PIP under your door, there were some conversations that had to happen before that occurred, and there may have been signs that this was coming, which should be examined. If not, that's problematic as well.