[StAnDeliver]

"They said, "we have to let you go." The HR guy then explained that if I sign this agreement, that it would be seen that I quit in lieu of termination. When I asked why I was being fired, I was told "performance". I am an at-will employee, so I assume that can mean anything."

Get. A. Lawyer.

This is boilerplate HR bs ("performance" satisfies at-will) and if it's so gd important to them to make it look like you quit, then you're in a position to negotiate your departure. But only with a lawyer.

[Sacajaweau]

People don’t know that when a former employee collects unemployment, the employer’s contribution goes up.