I do think GB has more leverage than NYJ:

A chunk of their fan base actively wants Woody Johnson to sell the team
Robert Saleh/Joe Douglas have a 11-23 record together and Zach Wilson as their QB. Their seats are warming up.
All this offseason cocktease with AR basically has set expectations with the fanbase
AR flat out says he wants to be a Jet

All those factors put a lot of pressure to get a deal done. If they don't they look incompetent.

GB will want to trade him before the draft, if they can't agree they also look stupid and greedy, and if there's anything GB hates it's bad PR of any kind. They are under some pressure as well but not as much.

If Rodgers isn't traded and retires before June 1 he counts $40M against the cap - same as if traded. If he retires after June 1 they can split across seasons... again, I believe that is same as if traded after June 1. As mentioned I think they get a deal done before the draft; they will want to exercise the 5th year option on Love in early May and they don't have the cap room for all this shenanigans.

It's possible Rodgers restructures his contract, but I doubt it. I think he's trying to keep things amicable but there are some hurt feelings and he's not likely to go out of his way to do GB any favors.

I'd like to see GB get as much as they can for Rodgers -- he's one of the all-time great Packers and he still has something in the tank. He'll certainly feel like he has something to prove. I'm not confident they'll pry away this year's R1 pick from the Jets, but I do think GB needs multiple picks and the more young talent they can accumulate around Jordan Love the better. If the future starts now, they better get to building it.