I think what you’re looking for is what is sometimes called a “dns load balancer”. Offerings like Azure Traffic Manager or AWS Route 53 do this. You can set up health checks that the service will use to determine if one of your locations is down and then automatically update the DNS record to point to the other one. You can also get clever and do things that allow the DNS to resolve the IP of whichever of your servers is physically closer so you get the best performance. I’m not sure what options there are for selfhosting a DNS service like this, however, these services are extremely affordable – pennies – and run on very reliable infrastructure, which is what you want.

I don’t expect companies to be doing that much anymore.