So I did find this UK gov site for the NHS' digital and technology arm that talks about how folks who got vaccinated in the US and have CDC Cards can use those cards as their NHS Covid Pass (though this site predates the most recent developments implementing the NHS Covid Pass for large events and venues in England):
https://www.nhsx.nhs.uk/covid-19-response/using-the-nhs-covid-pass/
It looks like the site is meant as guidance for merchants, venue operators, and others who need to review NHS Covid Passes.
I'm wondering, though, if anyone here has actual real world experience having to use your CDC card in lieu of an NHS Covid Pass (such as in Scotland, for instance, where the covid pass system has been in place for awhile now)?
While I don't anticipate going in to any nightclubs or large events, I have seen some posts online by museums and other sites that mention they're awaiting guidance on whether they need to require NHS Covid Passes (because they might have a 500+ person capacity, for instance).