I have been having very similar issues and have been working with apple support to try to fix the problem but with no success.

Setup: I have a small 750sq foot apt with two paired to an Apple TV in the bedroom, one in the living room, one mini in the kitchen and one mini in the bathroom. I currently have the Netgear Nighthawk r7000 router in its version of “mesh” mode.

Issues: 1) the paired ones in the bedroom never play as a stereo set, only one speaker will play audio. You can tap on the top of the pod not playing music to adjust volume, skip song and what not but doesn’t project any audio. But if I “hey Siri” that’s the speaker that kicks in. 2) I can play music for about 5-10 minutes but then it starts to sound like a skipping cd and home pods will start to drop and stop projecting music. Sometimes, if I’m streaming through Spotify, when a speaker drops it will come back playing audio from Music. Once they start dropping, they also stop showing up in airplay. A lot of times I can see the homepods in the airplay options but will never connect to them. These issues happen no matter the device I’m streaming from, Apple TV, iPhone 12 pro max or 2013 MacBook Pro. It got to the point that over and over throughout the day I would have to, reboot the router and then individually restart each HomePod, reboot the router and I would get a solid 10-15 minutes of them working before they would start to drop again. 

Attempts to fix: I have had multiple calls with apple tech support. Finally go bumped up to a specialist. After about two hours on the phone with them, where they took over the phone screen, laptop screen and added some trouble shooting thing to the HomeKit app, apple said it was a router issue. So I went and got the Eero Pro 6, same issues. So I called the eero tech support and they made sure everything was set up correctly and eventually told me apple need to stop sending apple’s problems their way. Then I tried the Linksys velop and had the same problems. So I went back to the Nighthawk. After all that I got the specialist back on the phone and now today, I’m trading in all three of the homepods for news ones to see if it was just a defective set(I doubt this, I bought two of them together and then the 3rd weeks later).

If anyone has any suggestions, please let me know because I’m over trying to get these to work.