Click on a Google Home device in the Google Home app
Then click on the settings (cogwheel top right on Android)
(Only works locally)
There you should see the firmware version at the bottom of that section
For me these problems started after app version 2.15 and the new firmware 1.42.180518
Google says it’s not really experimental firmware, but more as a pre-release firmware. It’s not beta
Could it be the rebranding from Google Home to Nest that was done in this in this firmware???
Looks like the issue (at least for me) is specific to folks using Google’s mesh routers - see here. Apparently a recent firmware update bricked the pucks’ ability to forward the multicast DNS records of each cast device between each other. The workaround is to disable all but a single puck, so that all cast devices (and HA) are connected to the same router, but it sounds like a firmware fix is on the way.