The customer select shipping green box should display the shipping rates and shipping method when using the UPS and USPS extensions.

RESULTS:
UPS:

USPS:

Overall: ✅ - no need for additional work
I was doing some WCS testing already so I tried USPS and confirmed that it's coming through OK as well:

Thanks for testing this, @frosso! Looks like we're good on this so I'll close it out.
Most helpful comment
RESULTS:
UPS:

USPS:

Overall: ✅ - no need for additional work