WebSockets have head-of-line blocking.
HTTP/2 does not.
HTTP/2 does not.
I thought that was the whole motivation for building HTTP/3 on QUIC (UDP)?
But your HTTP/2 reverse proxy won't block fast responses on slow responses.
As long as your WebSocket reverse proxy does the same, you're fine.
(And same stipulation for your client.)
Websockets don't really have an advantage here because typically websockets are implemented server-side as event based systems, and if a RPC paradigm is put on top of it has the same properties as HTTP/2 request/responses ordering. So if HTTP/2 doesn't have head of line blocking, then you can't argue that websockets do.