It's no more risky than anything else an already infected person may ship, which is why the parcel delivery companies likely already have sufficient mitigation efforts in place.

How has 21 and Me been dealing with vials of saliva making it to their lab?

Shipping biological hazards is a solved problem.

Likely something like how this at home mail in test handles those exact same risks:

https://www.cologuardtest.com/

The sample is sealed inside a heavy grade plastic container with a screw top lid.

The plastic container is sealed inside a heavy weight zip-lock bag already form fitted to the inside of the shipping box.

The shipping box itself is quite sturdy.

I suspect something similar for this new LabCorp test, just customized for a swab.