Spotrac has a little more on Rodgers contract.
https://www.spotrac.com/nfl/green-bay-packers/aaron-rodgers-3745/
If the Packers release Rodgers prior to June, they will save his $31,623,568 scheduled salary cap hit but the $99,778,568 dead money would hit the cap so it would cost $68,155,000 more against the cap than if Rodgers was still on the roster.
If the Packers trade Rodgers to the Jets and the Jets take over his contract, the Packers are left with $40,313,568 dead cap so $8,690 528 more against the cap than if he is still on the roster.
If the Packers would release Rodgers after June 1st it would be $75,298,568 in dead cap money against the 2023 cap which would mean $43,675,00 more against the cap than if they keep him. The other $24,480,000 is applied to the 2024 cap. In my mind, it would be better to keep him on the roster than to lose almost $44 million in cap space
If the Packers trade Rodgers after June 1st, they still have $40,313,568 dead cap hit but it can be taken as $15,833,568 in 2023 and $24,480,000 in 2024 so they would have an extra $15,790,000 to cover the cap this season. So a trade designated as June 2nd would clear the most cap space.
I assume retirement would leave dead cap money pretty much the same as if he was cut but I can't find anything definite.