They would have to get him to agree to re-negotiate his contract. Could he be willing to do that? Maybe? But most likely he'd want to get something out of it, like more guarantees in future years, otherwise he has no incentive.
The key here is... you can split bonus money in the existing contract however you want, you can't split the actual guaranteed salary. So the Jets could trade Zach Wilson and pay some of his bonus without him being involved. If his SALARY had been $5M... they would have had to have him re-negotiate in order to pay that.
Teams can't unilaterally change a contract to make the salary into bonus.
As to whether it happens all the time.... kind of? But not really, ususally the player is getting something in terms of guarantees or something else. So sometimes it's guaranteeing an extra year to get a trade to go through, sometimes (like with Diggs) they might get rid of un-guaranteed future years to let a guy hit FA earlier... but in all of those cases the player has to re-work the contract and he has to get something for it.
On the case of Jones... he has $81M guaranteed on his deal, if you want him to re-work the deal to convert some of his 2024-25 salary to roster bonus.... you have to give him something, whether that is adding money this year, or guaranteeing an extra year of Base in 2025-26, he doesn't have much incentive to just do you a solid.