[Feat]: Delegate to upstream remote-cli script

## What is your suggestion?

Right now we use the script in lib/vscode/bin/remote-cli inside the integrated terminal but we should use it from our own script as well because it provides more than our implementation.

## Why do you want this feature?

So things we have not implemented like `--wait` work even outside code-server and so we can remove our incomplete implementation.

## Are there any workarounds to get this functionality today?

Use an absolute path to run it. Or put it in your PATH but then you could not run the server since that script only allows interacting with existing instances of code-server.

## Are you interested in submitting a PR for this?

Yeah, will probably take this on.

## Implementation notes

Probably easiest to keep the existing logic but then instead of talking to the Code socket ourselves spawn the remote-cli script.

**Edit**: need to make sure it supports stdin as well, see https://github.com/coder/code-server/issues/5693