Dead cap is always "this season." Other than Post June 1 reasons, dead cap is only dead cap once the player is no longer on the team.
The Saints are probably the worst example of cap management in a while. Had they accepted a year of rebuild after Brees retired, they would have been fine. Instead, they kept thinking they were going to be competitive, and signed free agents to keep the window open.
Of course, they were a little cap tight, so they had to sign bargain, older players. And give them bonus spread over more years to afford them, typically with a void year or two. Those players eventually retired or were trash, giving them some dead cap to deal with.
AND still they deluded themselves and kept thinking they were going to be competitive, and signed free agents to keep the window open. They followed the same pattern and now with some restructure magic to ease the hits of their already existing and sometimes mediocre players.
Finally all of their dumb contracts are finally cleaned up. Next year will give them a ton of room. They should be competitive, but they need to not be stupid with any FAs spending. Since they will have so much cap space in 2027, the smart play would be lower signing bonuses coupled with higher than typical base salaries which could be guaranteed.