I'm sure some other users can give you better answers, but I'm a bit curious what you mean by "standard".
FWIW, Vim (and presumably emacs) can run terminals as well as do things like ssh and ftp. Though I'm pretty sure the easiest thing to do would just be to use the Ctrl-R pattern in vim and have it send curl requests in a different buffer. As far as I'm aware, all the major LLM platforms have APIs that can be accessed through curl (or any other way you want to to GET/PUT requests). Here's something I found with a quick Google search[0].
So I'm not sure there needs to be "a standard" so much as "can it do http requests?" which is yes. I mean with this I think you can also see it wouldn't be too hard to set up and connect to a LLM hosted on the LAN. Could do it all through ssh
[0] https://arjunaravind.in/blog/using-vim-as-a-http-client/