My assumptions:
Gute is saying we need #13, Jets are saying no way, so we wait.
We aren't getting #13. Frankly, the Jets would be dumb to give us #13. All they have to do is wait us out another month and we'll shut up about #13 and they'll still get their guy. We don't have any other trade partners and it's not like we're going to just walk away if this doesn't get done by May.
Gute doesn't want it to get to that point, because he'll want '23 draft capital. So this gets done either just prior to the draft, or even during the draft, when Gute runs out of time to wait.
Final deal something along the line of
'23; 2nd
'24: Conditional 3rd, becomes 2nd if the Jets make the playoffs and 1st if they make the Super Bowl.
'25: Conditional 4th, becomes 3rd if Rodgers plays in '24, 2nd if he plays and the Jets make the playoffs, 1st if he plays and they make the Super Bowl.