But surely it does? It is TCP, even with multiplexing

I thought that was the whole motivation for building HTTP/3 on QUIC (UDP)?

Yes you are right. With HTTP/2 responses can be sent out of order, but once they are sent down the pipe they have head of line blocking and have to arrive at that order, unlike QUIC.

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.

Well, yes. There is always some form of it on TCP.

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.)

h2 does have head-of-line blocking on the transport level.