The "facts" of the event are going to be presented if you go to trial. Prosecution presumably will do its best to paint you in a bad light. What do you have to say in your defense? "I feel terrible and I made a huge mistake" isn't a defense, it's a plea for clemency.

I suppose it is possible that you might get lenient treatment if you were exceptionally remorseful and contrite. Maybe. Or maybe the judge or jury will feel that "We Need To Send a Message."

You claim that you "didn't take anything." But (apparently) you are not being charged with the robbery. So you are in agreement with the Cops / Prosecutor on this. You seem perhaps to think that the assault charge is about the robbery (yes?) but it looks to me that the assault charge is about the threat to use deadly force ("I have a gun!") You should get this clarified with your lawyer. You should also know the differences in sentencing levels between "Assault 3" and "Assault 4."

Even if you did not really have a gun and did not physically harm anyone, the law may still consider that you committed Assault. It sounds like you are not being charged with the robbery... well, that's something good for you. But you were "involved" in a robbery and when the victims of that robbery pursued you, you shouted out that you had a gun. Have you gone on record agreeing to that?

If you haven't gone on record admitting that you shouted out that you had a gun, you could try lying under oath and claim that you did NOT say such a thing. And face two witnesses who will swear that you did say that. That might not work out well for you.

If you did claim to have a gun (even though you did not), in that situation the law might assume that the victims felt (or any ordinary person would feel) threatened. Such a threat might be classified as Assault.

The fact that you were charged with (felony) THIRD degree assault, with an offer to reduce it to "Assault 4 gross misdemeanor" suggests that somebody either is willing to give you a bit of a break (!?), or they figure that going to trial, and succeeding, with the 3rd degree assault charge might be difficult. (Why not charge you with FIRST, or SECOND degree assault... hey, you could be in a worse position than you are!)

So...

Go to trial and lose: you have a felony on your record. I think this is Bad.

Go to trial and get more leniency than the reduced charge offer... you'd be ahead. What would need to happen for you to get that better deal? How likely is that to happen?

If you take the offer: you have a "gross misdemeanor" on your record. (I'm guessing that's less bad than a felony but I don't actually understand the difference.)

Does your lawyer think you have any additional wiggle room? If you overflow with remorse, contrition and abject apologies... could you get 6 months of community service instead? Or something?

That's all I have for now.