Presuming that this was a connection (as it appears to be), the bag is covered by the Montreal Convention even though it was gate-checked on a domestic segment. Thus, OP is covered up to a fair market value of approximately $1,660. While OP was headed home and there are thus unlikely to be any interim needs, if there are, OP may make reasonable purchases and submit those to DL for reimbursement. Their value will reduce the ultimate $1,660 should the bag never turn up. At 20 days the bag is considered lost.
It really isn't OP's problem to worry about who scanned what and how the bag came not to be loaded. The reality is that if he dropped it on the jetway, it was not loaded at all, somehow fell off or got dropped on the ramp, or highly unlikely was left on the jetway and then picked up as part of the arrival of the next aircraft. Also possible that it was simply sent to baggage claim either at DTW or CVG.
If the bag tag is a mismatch, DL will eventually look for the secondary name tag and if that has fallen off too, in the bag.
Keep checking the tag # on the app as it may eventually come to be associated with the PRN when located (or not).