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).