Yes I had a feeling you would be, the unfortunate thing is if your manager didn’t have a discussion with you beforehand regarding your performance and then gave you a PIP, then they have made their decision already. I would be looking for a new role.
Also I would not mention any intention on leaving, once they hear that they won’t get rid of you with a payout because you already thinking about it. The situation you are in right now, and I am in a similar situation is I am not getting enough work assigned to me, and when that happens it reduces your ability to get promoted, pay rise, growth etc., which then forces you to leave on your own.
Also I have never heard of anyone negotiating their exit, unless you are on a fixed watertight contract and I don’t see a Full time/part time employee negotiating anything. The best you can hope for is a redundancy, but that comes down to your manager who would submit a list of names, and then that gets fed back up. I can’t see that happening to a single person, so they are probably looking at lawful ways to get rid of you Via this PIP.
I’d Make sure to keep all emails, and get everything put in writing to cover yourself for any potential unlawful termination or evidence of not being able to achieve your PIP.