They are. Why anyone is willing to adopt the delusion that a "personal improvement plan" is about improving anything I cannot understand. The circumstances are far less severe and consequential, but I can only compare it to a political dissident in a totalitarian state being tortured so long that he eventually believes he was undermining some righteous, just society with his actions.

You shouldn't take it as a personal insult or grievance against you, but the "personal improvement plan" is what HR came up with when your boss requested that you be let go. If you've committed a crime or violated some policy (no matter how trivial) you can be let go immediately. But in most of the United States, it is simply a bad decision (financially) to just let someone go. It is much better to have some documentation of their inadequacy. Hence the weekly meetings.

The person conducting these reviews (be it your boss, or someone else) is probably bored out of their mind that they must participate in these meetings. The phrase "what did I do to deserve this?" probably goes through their head each time they complete one. They don't care about your performance at all at this point. They may provide an objective review, or they may just copy in some boilerplate. Something that sounds great like "fails to meet established goals". It doesn't really matter.

Again, it is completely pointless to take any of this process as any sort of rational feedback. At this point, the decision was already made that you need to go. They just need some documentation before you are let go. I would take the fact that you are being let go as feedback, but stop there. The "personal improvement plan" isn't about you. It never has been.

If you're in a financial situation where you can, just resign. If you can't, that is understandable. But no one involved is going to be upset if you just resign. I'd offer 2 weeks, but they'll likely just counter with an immediate resignation. If anything, everyone will be at ease.