Hi
@Humanfly! Welcome to ASR.
There are lots of cheap(ish) AVRs with HDMI ARC in and Surround out, from brands like Denon, Yamaha, Onkyo, Sony etc, but they're basically all big, heavy, inefficient Class A/B units with at least five Amplifier channels inside.
You can buy cheap, small 3-channel Class D Amps, but there won't be a good way to feed them surround sound via HDMI.
You can buy small Class D Amps with Dolby decode via HDMI ARC (WiiM Amp Pro/UniFi PowerAmp), but the most that they can do is 2.1
WiiM are currently looking into wireless Dolby surround by combining multiple of their units, so that may be a way to go in the future, but for now I'm afraid the product that you're looking for does not exist.