I hadn't seen any mention of this ....
Has anyone thought to check the PiHole DNS logs to see whats being blocked to the Google-Home-Mini's ?
They are expected to "phone home" once in a while for updates/syncing.
When they can't call home they think the internet is down and start reconnecting.
Think of it as Googles way to ensure they get full access to the internet.
I have the same issue with other devices, Nest, Alexa, Dyson fans, to name but a few.
Exactly the same issue and results.