Inaccurate Work Eval. Should I Fight It Or Drop It?

Location: Missouri. I have been a manager at a public library for about 4 years. My 2025 eval was poor, so I didn't get a performance-based raise for this year. The eval was incomplete and inaccurate, though. All managers in the library system had the same issue, so I don't think it was personal. I feel like they are trying to make us all quit so they can hire new, cheaper managers.

An example of the feedback I received is under the technology section of my eval. It consists of one sentence. It says I make my own fliers using Canva. That's it. In reality, I learned AI processes in my field, online transcription and translation, photo editing, DNA testing, new online research processes, etc. Other sections have similar mistakes. I want these admitted inaccuracies (more on "admitted" below) off of my record bc they will effect future job opportunities. Also, the public, whose taxes fund the library, would agree.

I have a documented disability (narcolepsy) with accommodations, and also epilepsy. HR has documents from my dr saying that if I don't get enough rest, I am at risk for uncontrollable naps, etc. I am also at risk for a seizure, but I don't have accommodations for that bc they are controlled with medication. However, if I am sleep deprived, I am at risk for a seizure. As a direct result of this false eval, I have to work a lot of extra hours on a side hustle, so I am sleep deprived. I've been falling asleep a my desk at least once daily, I am not performing well, and I'm becoming a safety risk. I have intermittent FMLA for dr appointments, but I don't know how to use it in a way that will be useful on a daily basis.

I am going through the proper grievance procedure to request a correction, complete with a stack of documentation literally over an inch thick. I spoke with my supervisor, and he was embarrassed and said yes, he made some mistakes and accidentally left some things out. He talked to HR about changing them. HR refused because it was too late to change any evals. Supervisor apologized to me and said he would do better next time. The next step was HR. She said that yes, there were mistakes, but they weren't going to re-eval. I don't remember the reason right now, but it also was not true. Next step was executive director, who said that I was just doing what was expected of me last year, nothing special, so they weren't going to change anything. If I was doing only what was required, wouldn't I get an average eval instead of a bad eval??

As it sits, my records show that I suck. When a future supervisor sees my eval, they are going to think that my only technological ability is making fliers. Should I just drop it? MO is at-will, so I'll get fired for retaliation but not RETALIATION retaliation anyway, so I want to pre-emptively quit, but would I be able to get unemployment? I'm a single mom, so I am paralyzed with fear of making the wrong move and not being able to support my kids.

What do I do? TIA