!htp #16162 Upgrade server- and client-side HTTP APIs to "final style"

This PR clears #16162.
It currently builds on #16383, so ignore Björn's commit in your review.

As a temporary measure I have added a stub TCP API as described by #16166. This `TempTcp` stuff will go away when #16166 is cleared.
There is probably a pure-stream solution hidden somewhere here, yes.
I'll add a FIXME to iron things out.