Saints sign Chase Young to 1-year deal up to 13M (2.7M base, 1.86M signing, 450K workout, 7.99M total gameday roster bonus)

They might get a comp pick, but they're absolutely not getting a 3rd round pick back.
Right now they are projected to get a 5th rounder. They lost Young and Darnold for 5th round AAV, and signed Leonard Floyd at an AAV that cancels one of those two picks.

I would assume that Young’s value gets recalculated based on actual earnings, so they may not get much if anything when it’s decided next offseason. We should actually want them to get a 5th, that means he played all season for us.