Ring is owned by Amazon. So is Eero. I currently have both. My Eero mesh WiFi network is great and does a great job keeping my outdoor Ring devices connected for the most part.
But I think that anything that has constant power (such as wired spotlight cams) should integrate eero mesh beacons so that your home network signal strength and coverage gets even better. Same thing with smoke detectors. How great would it be for there to be a Ring smoke detector that obviously ties into your Ring security system, but was also an Eero beacon that always had power without being plugged in and sitting on a shelf, counter or handing from the wall outlet like the current beacon does.
Not only would you get to the benefits that each provides individually, but every “Eero equipped” outdoor Ring device would provide that much more wireless coverage for the next one. Now you can not only extend WiFi to remote areas of larger properties, but provide that needed WiFi coverage for even more additional Ring security devices at those further ends. At the same time, integrate a Ring z wave extender so you can have sensors at those further away locations.