Integrate existing Nest thermostat & cameras with Ring & Alexa

I have some Nest cameras and a Nest thermostat. I also use Alexa Echo and Dot. I want to switch from Nest to Ring so now I have a Ring doorbell and some cameras. But I’m wondering if I absolu have to swap out my old Nest thermostat etc or if I can integrate them with Ring all together under Alexa or Ring (not under Nest, I want to move away from Google because although they’re great at projects they abandon projects often and I don’t want my smart home system dependent on such fickleness). Any ideas?