Class D and AirPlay

RPi is overkill. I use a WT3020H (or F) router running OpenWRT + shairport-sync, plus a little USB DAC. The router is tiny, and you can remove the case if you'd like it to be smaller.

There are some even smaller options, but either know the software sucks, or suspect it does. I have a Sabrent WF-RADU & an iReceiver. Both are based on the same Ralink WiFi SoC, both run an embedded Linux firmware with shairport (the less capable predecessor to shairport-sync). Both have a DAC chip onboard (Everest Semiconductor for the Sabrent, Wolfson for the iReceiver). The problem is that the firmware for both is kind of junky. I've found backdoors into both, but haven't gotten any further in my plan to get either of them running OpenWRT. There are a few other options too, but as I say, I don't know whether they are better or worse.

A thrift-store airport express is probably the cheapest/best quality option. For compactness, the router/DAC combo I suggested. If you want a nicer DAC, one of the HiFiDIY ES9023 would be a compact option.

Whether you use a router or an RPi, you'll probably need a DC-DC power supply module to buck down from the amp power to 5v USB power. There are lots of options I don't have any suggestions.

A Raspberry Pi works well enough, doesn't need to be the latest and greatest version 3 model B. Even a RPi Zero would work (though you'd need to use a little USB hub as well). If you can find a model A that's a good and inexpensive compromise. I can't speak for other parts of the planet but over here even a first gen Airport Express B/G only is more expensive than a Pi, they tend to keep their value somewhat. There's tons of options for DACs suitable for a Pi, from DIY options on eBay or diyinhk.com to DACs that mount directly on the Pi, like the HifiBerry.

Also, the Pi not only allows you to run shairport but you can run something like RuneAudio or Volumio, which are versatile audio players, with iOS/Android remote control apps, can play networked and local content, webradios, etc etc.

With some careful planning you can mount something like a TPA3xxx amp and a Pi in one of those small eBay pre-amp enclosures and (using a step down convertor to 5V) power both off a laptop brick for example. There's lots of nice builds and examples to be found.

Any Airport Express works well of course and is really easy to set up. But if you prefer to do something with your hands a Pi based media player/amp combination is a nice and rewarding project in my opinion.

Yeah, I know what you mean. I wish there was a good, easily embedded, option for a reasonable price.

I think I'll start a thread here to see if there is anyone with relevant experience who could help me get openWRT (& shairport-sync) running on the $12 iReceiver. It has a WiFi SoC + a Wolfson WM8960 codec onboard.

There are sub plate amps with signal sensing power on/off functions. Perhaps one of those circuits could be copied for your project.