This is super helpful for companies that have tight security constraints. At work, I am forced to work in an air-gapped environment to prevent unwanted stuff from coming into our network and also to prevent stuff to leave our network.
Setting up the remote Extension is a pain in the A$$, because it is not possible to install the server by hand. It is side loaded by the extension. So I have to download the extension manually and scp it to ~/.vscode-server/bin/${commit_id}.
I'm not sure this is going to work for you though, it seems to make you go through a tunnel service that MS is running on vscode.dev. Look at the flow they describe and it has you getting an auth code after github login and using that code on vscode.dev to access the server instance.
If you haven't seen it already coder has a nice VS code server instance that runs like a traditional self-hosted server app and could likely be run in an airgapped environment: https://github.com/coder/code-server