> be to re-implement the Electron API's that Code uses in HTML5 Javascript with local storage, such that VS Code could run entirely as a HTML5 web application.

This does not look fancy. Microsoft uses VSCode for their online Editor in Azure and VSS: - https://channel9.msdn.com/Series/Visual-Studio-Online-Monaco

Or to say it differently, at least the Editor part is working directly inside the browser: - https://github.com/Microsoft/monaco-editor

(P.S.: I'm not related to Microsoft, I just tumbled upon while trying to work with App Services on Azure)