Most smart doorbells (e.g. Google Nest Hello doorbell) seem to require a wired connection. The Ring wireless doorbell looks like the most popular but compatibility with Google Assistant looks poor. I can't tell if Ring would chime on Google Nest but it looks like I can only ask Assistant to tell me things rather than it proactively do them...
I want a wireless (i.e. battery powered and wifi) doorbell that chimes on my Google Nest speaker and I can also access video (separately, not on Google).
Scroll down that link to Nest doorbell
It has WiFi for network connectivity, it just requires wired power.
Also expecting Ring (an Amazon company) to work well with it's main competitor's products is possibly asking a little much
If you just want it to be wireless so that you don't lose it when the power goes down, I would recommend getting a UPS/APC and using the Google Nest Hello Doorbell.
According to Google, the Nest Hello Doorbell never draws more than 9W. With an APC like the BE650G1, that means you'll have power on your device for well over 6 hours, which should cover most power outages.
