Currently addresses parts of T7972
Fixes T7726. More related issues could be addressed, but the diff is large enough, already, so I think it's a good idea to review that, before proceeding.
Some of the diff, esp. in webserver.cpp is somewhat unrelated, but seemed very much worth while, while modifying some of the protocol: There was a huge amount of boilerplate code around sending commands between proxy and the clients, so I factored some of that out.