If they don't say, it's probably class AB since that's been standard since almost the beginning of hi-fi (for power amplifiers... amplifiers that drive speakers).
But I think most AVRs are class D because you can make a powerful multi-channel amplifier cheaply, and they may not advertise the amplifier class.
Class A, AB, and D are all fine for audio, and any good design will be better than human hearing. Some of those other classes are not suitable for audio, but I don't remember what they all are...
Class A is very energy inefficient. The main output MOSFET (or transistor or tube) burns more power than goes the speaker even when it's idling with no sound. You won't find a 200W class A amplifier. It's OK for preamps and
maybe OK for a headphone amp, but for a power amp it's a "dumb design".
On the other hand, class D is very efficient with most of the energy going to the speaker.
Efficiency is important and energy savings is a just side-benefit. The main advantage is that the wasted energy is converted to heat and heat is what burns-up semiconductors. So with a given MOSFET (or other device) and class D you can get
more audio power to the speakers and you can get-by with smaller heatsinks. Almost all high-power pro amplifiers are now class D. High-power class AB amplifiers sometimes use multiple MOSFETs in parallel to share the load.
Class D is more complex but since most of the complexity is built-into a microchip it's often cheaper to make a class-D with power and performance similar to a class AB.
The "audiophile community" is mostly nuts! For the most part they don't trust measurements or blind listening tests and they don't accept that there are real limits to human hearing. And, they tend to use lots of meaningless words that often express a feeling instead of using scientific-engineering terminology like noise, distortion, or frequency response.
And there is a sub-group of "audiophiles" that are fascinated with vacuum tubes and vinyl records, and maybe other nostalgic technology. Tubes can be as-good as solid state electronics but it's more expensive and MUCH more expensive if you want to make a good tube power amplifier. A record is technically inferior to digital audio in every way (noise, distortion and frequency response).