Mark, HDMI is not within the regulation purview of any US federal agency I'm aware of, and since most of these products are designed and manufactured outside the US you'd be talking about regulation in each individual country. (I'm honestly not sure what would happen in an entity like the EU.) Having had a lot of experience in these industry specification groups for computing, they operate for the benefit of "adopters", and while they mandate testing to protect their specification brand, the testing they specify is usually not rigorously monitored or enforced. Here's the testing policy for HDMI:
HDMI Compliance Test Specifications provide a suite of testing procedures, HDMI 2.1b
www.hdmi.org
Full of more holes than a block of Swiss cheese. I especially like this quote:
"Successful completion of the Compliance Test Specification or ATC Testing does not guarantee that any product will conform to the High-Definition Multimedia Interfaces, function correctly or interoperate with any other product."
I can't speak with experience about these standards for audio/video, but in the computing industry a lot of prototype interoperability testing is in "plugfests" that are organized by the industry specification group, but they are interoperability workshops, not compliance enforcement venues. These industry groups assume that non-compliant products will get fixed or die from failed integration testing in higher-level device engineering. In computing these industry specifications developed by private "trade associations'" include PCI Express (PCI SIG), NVMe (nvmexpress.org), DDR (JEDEC), IPMI, InfiniBand (IBTA)... I could go on and on, there are so many of them. The associations all look alike in a lot of ways. You join and pay to become a member to contribute to the specs and get a license, or you can just license them as an adopter for so-called reasonable and non-discriminatory (RND) license fees for the intellectual property.
Also, it is important to differentiate between "industry standards", which are developed by independent groups, like the IEEE, IETF, ANSI, INCITS, etc, and these pay to join industry groups. HDMI is not an industry standard as is, say, IEEE 802.1/.3 Ethernet, it is an industry specification that is owned by a trade association.