Before I go any further, I should point out that while Pete Carroll is the NFL's oldest coach at 72, he certainly doesn't behave on the football field like however one would assume a 72 would act. Carroll is as active as any player on the sidelines, throws the ball with players on the field before the games, and runs around like a 25 year old. I point all this out because if a team wants to take a chance of getting a very good coach, Pete Carroll's age is likely not going to scare them off from trying to trade for him.
Also, half the times teams have traded for a head coach the team wanting the coach has given up a first-round choice. The three times that has happened since 1997, including when the Denver Broncos traded for Sean Payton last year, the team has given up multiple picks, not just one first-round pick. I think Seattle would be OK with one first-round choice, though, as long as the pick is high in the draft.
The Bears, who will still need to terminate Matt Eberflus, are going to have two very high picks in the 2024 NFL Draft as things stand. They will have the first pick, which they got from the Carolina Panthers during a trade in the 2023 NFL Draft and Carolina has been awful this year, and will probably have a second choice between picks 6 and 10. The Seahawks should ask for the second of those two selections.
The Bears would be getting a proven coach who knows how to get young quarterbacks to be better. No one expected Russell Wilson to turn out to be Russell Wilson, and while Carroll doesn't coach the offense, he knows how to pick offensive coordinaotrs who work well with quarterbacks. Except for 2023, quarterback play since Carroll arrived in 2010 has been mostly very good. Should Chicago either draft a QB or keep Justin Fields, Carroll is probably going to find a way to maximize their abilities.