Quit Or Stay? PIP, A Bad Manager, Family Trouble

Hope everyone is doing well and gainfully employed. Recently I was put on an informal PIP (performance improvement plan), with the only next step to check in with my manager in 2 weeks to discuss my plans and response to it, so nothing definite about termination as it sometimes can be, but I'm worried regardless.

Some background: Took this job around a year ago at aREPEfirm (30-45 people total), mainly to gain exposure to an asset class in which they have yet to close a deal (not likely not in this environment and maybe even ever). The primary asset class is very niche in my opinion and is otherwise completely uninteresting personally and I'm afraid of getting pigeon-holed. I have liked my experience so far as it's on the equity side so I've learned a lot, and generally like most people that I work with.

The issues:

1. My manager has gotten very difficult to work with as I received a less than stellar review last year. They're generally nice when it doesn't come to work and I try to make small talk with them when I can. I admit that I've not been as good as I can be, and they've acknowledged some improvements I've made, but a large part of it has been their cold and unprofessional style. More recently they've been constantly berating me and belittling me, to the point that it's very insulting. I try to brush this off mostly so it's not the worst thing, but for me it's getting progressively stressful. However, the info in the PIP is self-contradictory. At our preliminary talk about it, I've mentioned that at times their instructions aren't very clear and they believe I follow them improperly, even though I have recorded evidence (chat history, emails) that show where I clarify them, but they instead said my comprehension of it was low. There have been other situations like this where I've performed my duties, and I've confirmed with other coworkers that they thought I did a good job, and yet my manager instead micromanaged and did not share the same sentiment.
2. There has been seemingly a lot of turnover in the past year since I've joined, particularly at my level (asset/portfolio management, but also across the firm). Some of the other analysts told me in passing that some of the managers have very unrealistic expectations (they seem nice to me but I don't work with them as frequently and can only speak about mine).
3. I'm not interested in this asset class at all, it's not stimulating at all, and working from home has made me think of leaving overall, which I was planning to do anyway but not at an accelerated pace.
4. 尽管我一般不与我们的高级交互management, a former mentor of mine that used to work here coincidentally (has since left to a different market) told me that they are very self-serving and rude individuals. I can't confirm or deny this yet as I haven't had to interact with them much, but it doesn't help.
5. I recently found out that my father has been diagnosed with cancer and at best has less than a year to live. I haven't disclosed this to anyone at work (only a few of my very close friends and extended family), but I feel like this has very significantly impacted my recent performance. I'm generally soft-spoken in the workplace and would rather not disclose this to anyone that I work with so that they don't think that I'm using it as leverage in some kind of way. I also don't know what I'd do if I lost my job without something else lined up and having to either choose to lie to my father or telling him that I'm unemployed given his situation.

我要做的everything I can in the PIP since it seems like it's more informal and doesn't put me on a worse trajectory, and I believe there is some good stuff in there that will help me be better generally. I need to cool off, vent, and work on some things. However, at the end of the day I'm not sure how they'll act even if I follow it to a T. I'm afraid of losing my job for obvious reasons, but particularly given COVID if it comes to it, I need to make sure that I can at least get unemployment benefits while I look for work.

Has anyone been in a situation like this?