The backup is usually a different server from the same DNS provider. E.g. google has 8.8.8.8 as primary and 8.8.4.4 as secondary. Plus the backup doesn't even always work on Windows.

Also note, it is not browsers but operating systems that do primary DNS. Browsers may use DNS over HTTPS for security and privacy instead of the one in the OS, but that usually requires the OS DNS to resolve the address of the DNS over HTTPS server, since it is considered a security feature built on top of classic DNS instead of replacement.

PS: Don't get me wrong, EU could definitely block google.com sooner or later. It just wouldn't be as easy as usual. The real risk is if Alphabet stops offering all of its services, chaos ensues. Companies unable to access their google spreadsheets. Services and data hosted on google cloud lost. People protesting lack of youtube...

And even if Alphabet doesn't do that, I expect a lot of issues just with google being unavailable and most people not even knowing there are other search engines. It's really going to be last resort to try blocking google, I expect fines or some such.