Tell them nothing and break off contact, make sure any property of theirs is returned (you did that). File for unemployment regardless of any severance package that may or may not be issued/promised.

Yes they're trying to do the shitty thing and go back on their 'no contest' word. Do not let them. Once you file they have a limited time to answer/contest the claim. Anything you say to them or give them in writing could be used against you.

Even if you were fired depending on the state you can still get unemployment compensation. For example, in my state (Ohio), if you answer honestly and state your case you may still be eligible. I claimed honestly recently insomuch as I was terminated but because the company was not able to establish objective 'just cause' the state ruled in my favor without needing to advance to an appeals process, e.g.: the company did actively attempt to block the claim within the time period allotted and failed to establish just cause for terminating me, I get benefits that the company has to pay. Despite being a 'right to work' state it is necessary to have reasoning that a third party would objectively see as damaging or harmful to the company to 'fire' someone.

TLDR: They ended the relationship, trust nothing they say, you have all the cards at this point don't show them any.