File. Make them tell you no.
I agree with blue. The state government -- elected by you -- runs unemploymenmt. They don;t have feelings, like "this guy is over-reaching".
Further, there is, and has always been, seasonal unemployment and unemployment during a temporary plant shutdown. That's what you have: the place of business is closed, it might re-open, but unless they are paying you right now, you are officially unemployed.
If the restaurant offers you work because you are registered as unemployed, that's good. It happened to me years ago when my taxi garage closed. I filed for unemployment, collected for about a month, and got a call from another garage (friends of my former boss) offering me work. No big deal, nothing personal.
UNless somene knows something astonishing, I would file.