He didn't agree to a trade last time with the Raiders. Carr will not give up any money or control. He would probably require the team to release him in that situation.
Then, the question would be who would blink first if you make him the backup in 2025 behind Rattler, Haener, or another veteran that you bring in...
His 2026 his cap number gets a lot better for the Saints to release him after June 1, 2026.
My personal opinion due to his age is that he will not want to lose a year of playing backup QB...