No, I think that you have that wrong.
When a player is cut, there are only two options re dead money... (1) pre-June 1st cut requires all dead money (remaining prorated signing bonus amounts) goes against that year's cap, or (2) designating the cut as post-June 1st, which allows the dead money to be split over this year and next year.
There is no case that I know of where there is dead money for cutting a player that extends to year 3 or beyond. It all comes due in the first year (pre-June 1st cut) or is split between year 1 and year 2 (again, for a post June 1st cut, whether designated or not).
In Carr's case, if he is a pre-June 1st cut, his dead money will be $5.625M... and it will all go against the Raiders 2023 cap. After this year, he is totally off the books for the Raiders.