FCC/ETSI conformance with backscatter
Of course, all emitters fall under the rules of the local regulatory body (which seems to be FCC in your case), unless there's a specific norm that exempts them (which seems to be the case in the US for tags, if you're reading that policy right).

ETSI is not a regulatory body, but a standardization organization, so they have nothing to do with this; the document you're linking to is a recommendation on how to technically implement the respective EU directive (and it's up to the EU member state to convert that directive into law; they can, but don't have to refer to an ETSI standard in the laws they formulate).

So, you'd need to read that EU directive, Directive 2014/53/EU, and then check whether and how the individual member states implement that directive.

Again, the ETSI doesn't have any powers here, they just propose a technical standard.