Linked test project contains already set up actor as described in steps to reproduce. Using a kinematic body on a root bone, setting all other bodies sleep family to Custom, and their custom sleep threshold to 1000000. You will notice when simulating that the kinematic root body will prevent the skeletal mesh from sleeping. There is an actor using exactly the same physics asset except it has no constraint. This actor falls asleep as intended.
This issue was reported and tested in 4.21.2 (CL-4753647). It was reproduced in 4.20.3 (CL-4369336), 4.22 (CL-5275346), and Main 4.23 (CL-5295869)
Results: Skeletal mesh fails to sleep.
Expected: Constraint does not prevent skeletal mesh from sleeping.
There's no existing public thread on this issue, so head over to Questions & Answers just mention UE-71059 in the post.