I have a couple RPi ZeroWs running balenaSound with a custom build. You have to strip it down to only the multi-room client, audio and sound-supervisor containers (it’s not enough to just stop the containers on a default build). My RPi ZeroW which also has a Pirate Audio line-out DAC /w OLED screen consumes about 260mA max while running. It bounces around between about 180-250mA at 5V.
In fact, both of my ZeroWs are slated to be integrated with the old Sony CD/iPod boom boxes they are currently attached to. I’m going to install them internal to the boomboxes, and power them from the battery/plug power, so I don’t have to keep them plugged into USB separately.
Also, check out this thread: Snapcast client container direct to audio output in multi-room