QUIC does require TLS 1.3, but as far as I can tell HTTP/2 over TLS 1.3 is perfectly viable, and is likely a common deployment scenario.
Upgrading just TLS to 1.3 for most people likely just means upgrading to a newer openssl which you probably want to do anyway. In many web server deployment scenarios, deploying HTTP/3 is highly likely to be more involved. The Apache httpd doesn't support H3 at all, I don't know if nginx has it enabled by default these days?
NGINX has an experimental QUIC branch [1], but in my experience it is buggy and currently has lower throughput than using Quiche [2] with NGINX. I do the latter for my fork of NGINX called Zestginx [3], which supports HTTP/3 amongst a bunch of other features.
NGINX's QUIC implementation seems to also lack support for QUIC and or HTTP/3 features (such as Adaptive Reordering Thresholds and marking large frames instead of closing the connection).
EDIT: A friend of mine who works at VK ("the Russian Facebook") informed me that they're helping out with the NGINX QUIC implementation which is nice to hear, as having a company backing such work does solidify the route a little.
Upgrading just TLS to 1.3 for most people likely just means upgrading to a newer openssl which you probably want to do anyway. In many web server deployment scenarios, deploying HTTP/3 is highly likely to be more involved. The Apache httpd doesn't support H3 at all, I don't know if nginx has it enabled by default these days?