I don't know the VS Code add in, or anything...
But:
couldn't create connection to server.
From what I gathered (read a good while back somewhere), the Language server is basically a wrapper for the Lazarus codetools (at least one VS extensions, IIRC the one by Joost V.d.S., does use that).
If that is the case, then it needs to run as a separate app in the background. And may or may not need its own config too.
As I said, nothing of this is for sure. But maybe, with the help of some search engine, this leads you to some docs that will help.