If OTC is correct and up-to-date, Carr is a $20M dead cap to move him post June 1. And he's a $20M cap hit if he stays, so the money is already allocated without further cap spending. Saints would just be deciding to spend that money to not have Carr.
Watson's cap and dead caps are insane and hilarious to look at, until 2027, when it finally drops into the 20M's. They are stuck with him. He is rehabbing but not expected back in 2025 as he recently re-tore the achilles. As posted by others, they must do something draft or trade for a vet.