Ring and Google/Nest used to be on the path for compatibility, but it was gutted when Ring was acquired by Amazon. Some left over integration may still be present, like checking battery level or other useless capability, but the key feature of streaming the video from camera or announcing a doorbell press is not present.
I don’t know who’s fault is it, and each side will point the finger to the other. Howver, given how almost all other device can work with both Google and Amazon (and so did Ring before Amazon bought them out), I would say it is Amazon / Ring that is relunctant to do what it takes to integrate in.
I still have my Ring Cameras and Alarm, but have recently switched all my Alexa echo and echo show to Google Home / Nest Hub. Camera and alarm may have to go if they continue to be incompatible. Google has superiority access to web / video content, and much nicer screen based devices (the echo show 5 is so slow). It is too bad because Amazon / Ring does have a very nice alarm system and better home automation, it just that their screen based device suck and lack of YouTube / web search really hurts the assistant.