The client and its scripts and plugins get unrestricted access to the remote system.
The code you’re editing (if not in restricted mode) gets full access to the system it’s on (which is IMO an unfortunate default but not surprising — it’s really time for development systems to wake up and sandbox the code being developed to at least be limited to its own directory tree, but that’s a different story).
The code you’re editing (if not in restricted mode) and remote plugins (no prompt at all AFAICT) get effectively full access to the client system, subject only to whatever privileges the client itself has. Yes, you read that right, if you Remote-SSH into a machine, that machine immediately owns you. Microsoft knows, and they do not care.
See, for example, https://github.com/microsoft/vscode-remote-release/issues/66...