California- Employer Lied And Said To The Unemployment Agency I Was Fired When I Was Not.

Company forced me out of the company essentially. No performance issues or PIPs or attendance issues ever. They planned my exit while I was out on an approved leave of absence. Literally the day I can back they presented me an offer to exit the company pretty much threatening me to leave. We agreed on a lot of things in writing and I signed a general release to not sue as I experienced discrimination overtime and had proof.
Now I filed for unemployment and the company put in writing TO ME that the reason for separation would be "mutual agreement NO MISCONDUCT" but to the CA STATE they have told unemployment that they fired me. Now this is impacting my unemployment pay. The Unemployment representative said they see the company submitted a paper saying reason for termination was "FIRED" and nothing else.
I am concerned that if they would tell the CA STATE unemployment office this that they would say this to prospective employers on a reference check as well. I do believe this to be libelous. That's not the termination reason we agreed on at all and how is that accurate? I put on my end laid off as that was more close to what happened but the point is they are saying I was fired and that's a big deal. I also have in writing where they said I was eligible for rehire! So that doesn't add up.
What should I do as a recommendation??
I have all emails and screenshots of my claims of what took place as well from my HR contacts who told me all this during my offboarding and who I coordinated with to sign all legal agreements including the general release and other agreements.
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