HTTP had persistent connections ever since HTTP/1.1, and HTTP/2 supports parallel streams within the same persistent connection.
HTTP/3 is still a IETF draft, but is already being deployed pretty much by all big sites. It supports zero-round-trip (0RTT) requests even after the IP of the client has changed.
DoH can essentially match the latency of traditional UDP queries, while also encrypting the channel and traversing any gateways that let HTTPS through.
You can't get 0-RTT with TCP because the TCP handshake itself isn't 0-RTT. HTTP/3 accomplishes it by switching to UDP -- but then you can't get through the legacy middleboxes that only allow HTTPS over TCP port 443.
HTTP/3 is still a IETF draft, but is already being deployed pretty much by all big sites. It supports zero-round-trip (0RTT) requests even after the IP of the client has changed.
DoH can essentially match the latency of traditional UDP queries, while also encrypting the channel and traversing any gateways that let HTTPS through.