I didn't hear him say he only wants to play for the Jets. Rodgers is not a dumb guy, and is aware these deals can and frequently do go sideways. That is why he said he intends to play in '23 and intends to play for the Jets. I doubted he was ever going to walk away from 58+ million dollars in '23 for just showing up.
Thus, the Packers could trade him to any QB needy team (Commanders, Falcons, Titans, etc.) with virtually no risk. Acquiring team gives the Packers conditional picks if they can convince Rodgers to show up. If they can't they're not out anything, nor are the Packers as Rodgers would be retired.