Your domain is "hosted" (in this context, the DNS entries, not the actual content) on one or, ideally, more DNS servers that are known as the authoritative servers for your domain. You can look those up by searching the SOA (start of authority) and NS (nameserver) records for it.

Downstream servers may keep those and other records in cache for a while, usually guided by the TTL (time to live) entry. Once that expires, however, they need to refresh the data from the authoritative servers.

When those are unreachable, that cannot do so, and your domain is de facto unreachable for the internet at large, regardless of your own server actually being up.

You can still reach them by surfing to the actual IP instead, and/or hardcoding the DNS name in your local hosts file or your local DNS server/resolver. That is, of course, not visible to the internet at large.

You could host your own DNS servers to mitigate somewhat, but keep in mind that every level above your domain also needs to know which server is authoritative - my tuxera.be used to be self hosted, so the .be root servers had to know what the SOA for tuxera was.

Honestly, it's not something to worry about. I didn't keep up with changes in DNS security, so i switched to route53 (Amazon). I've been considering switching again to hetzner.de where i have some servers anyway.

DNS is pretty lightweight (relatively speaking), so it's probably the last thing to go down if a registrar is in trouble; you'd have plenty of warning signs beforehand.

(Yes, for pedantry, technically a registrar doesn't even have to offer DNS at all, they just handle ownership and administration at the top level domain, but most do anyway)