The server component was already open sourced (this is the -same- server/remote component that was previously powering all of the remote development extensions). It's here in the main vscode repo (https://github.com/microsoft/vscode/tree/main/src/vs/server).
There's vscode.dev (running vscode in the browser). That's apparently just a specific web compilation of the main vscode repo. There are alternate web compilations sitting around (for example https://github.com/Felx-B/vscode-web).
Open VS Code Server takes this barebones implementation and fleshes it out enough to be minimally usable: https://github.com/gitpod-io/openvscode-server (i.e. run it from a CLI command, do basic token auth, etc.)
Coder's code-server (what you link) is similar to open vs code server but predates it and has a bit nicer server implementation, like it can be configured to run behind a reverse proxy or under different web paths more easily. I really like the linuxserver.io container that packages it up and runs it with ease: https://hub.docker.com/r/linuxserver/code-server
For anyone that stumbles upon this later, I strongly recommend gitpod's openvscode-server container over coder's code-server. Linuxserver.io has docker containers for both.
openvscode-server has had 1:1 parity with a full desktop install of vscode, while coder's variant always had issues with several official plugins.
In coder's implementation several menu options will trigger caught exceptions for basic shit like opening a jupyter notebook, typescript language server frequently crashing, environment variables not being set properly in the correct order of priority, etc.
openvscode-server "just works" on the other hand.
Note that with both implementations the easiest way to get access to the microsoft plugins store is to compile it from source and modify preferences.json. Open source maintainers technically cant distribute it this way out of the box due to Microsoft's licensing requirements. Alternatively, you can always just download the extensions in your browser and drag and drop them into your vscode server window and install them that way.
When using linuxserver.io's container for openvscode-server, traefik worked fine as a reverse proxy to put it behind an https domain I own
There's vscode.dev (running vscode in the browser). That's apparently just a specific web compilation of the main vscode repo. There are alternate web compilations sitting around (for example https://github.com/Felx-B/vscode-web).