But finding more information to settle it would take googling in a desktop for a few hours chasing down weird Chinese forum rabbit holes.

I think there are ICs for that specific purpose? If I understood your second paragraph correctly.

But to test, for you? You can try a regular/non-special, cheap ground loop isolator. The car audio section on Amazon is full of them. You ideally want one that just has transformers inside of it; these will be wound with a 1:1 ratio. They don't cost much; it's generally cheaper to buy them pre-assembled in a box with connectors than to pick up the parts individually and DIY it.

What you've read about transformers is correct: Transformers are imperfect. All of them are imperfect. They're measurably flawed. But if it works and you don't hear a problem with it, then: There is no problem.

Transformers are also the simplest way to add balanced audio inputs or outputs for...well, anything. :) Using different turns ratios (as DI boxes do) instead of 1:1 also allows conversion of impedance and voltage, which is useful.

(To cover another thing to mentioned in your writeup: HDMI audio is part of the video bitstream. It's not separate at all. So, yeah: The audio extractors that exist definitely operate on all of the bits. They don't get a choice in this matter. They also, ideally, intercept the EDID line so they can request only the formats that they can decode: This can be a fun way to encounter what I'd like to call "unexpected learning opportunities".)

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[1]: One of the things I used to do was help install residential AV systems for a small local shop. We'd sometimes have customers with surround systems that worked great for years, until they had us back to add a powered subwoofer. And then it was 60-cycle hum central.

In those cases, what I invariably found was this: The new subwoofer was the first component in the system that had a 3-prong plug, and this introduced a new connection to the home's electrical ground where there had been none before for that AV system.

Which should not ever be a problem at all, except: The cable TV or satellite line was grounded elsewhere (sometimes to a water pipe or whatever, sometimes a separate ground rod), and not bonded to the normal ground at all except through the AV system.

That's a violation according to the NEC, but it was often this way anyhow.

The correct fix was to eliminate the problem, and there's plenty of wrong and grey ways to do that... but the Right Way to eliminate it is to call the TV service provider and throw a fit until they finally send someone out to make their ground connection something other than illegal. :)

After that, the hum is gone (and the AV system is also better-protected against lightning damage, but that's a different topic).