HTTP2 solves these problems. HTTP3 (QUIC) solves the head of line blocking problem of TCP. That is, a packet getting corrupted or lost causes TCP to hold up other packets from going out until that packet can be successfully delivered. So you may be multiplexed in your messages, but you end up with a slowdown and backlog of data that could have been successfully received and interpreted but for the lost packet.

SCTP solved them. We're just rarely allowed to use it because the internet is broken.

Yes, it's a bummer that we have to encapsulate it in UDP, but when using it like that, it works quite well in my experience.

QUIC is HTTP/3 more or less and solves the same problems, yes.

Somewhat. Http/3 is a protocol that runs on top of QUIC. Every http/3 request uses a dedicated QUIC stream. However it is possible to use QUIC for other use cases that have nothing to do with HTTP. QUIC is more of a multiplexed TCP with mandatory encryption.