Make the VSCode extension compatible with https://vscode.dev/ and https://github.dev/

[beingminimal]

Is your feature request related to a problem? Please describe.
Developers are not able to use this extension with https://vscode.dev/ and https://github.dev/

Describe the solution you'd like:
Make the VSCode extension compatible with https://vscode.dev/ and https://github.dev/
@allevato @thomasvl @dierksen @reinhillmann @philwo @fweikert
Please consider this as DX improvement and give some priority for it.
Thanks

Describe alternatives you've considered:

No alternatives available.

Additional context:

Here is more info
https://aka.ms/vscode-web-extensions-guide
https://code.visualstudio.com/api/extension-guides/web-extensions

Screenshot of extension showing not compatible with web version.

[cameron-martin]

Are you expecting all features to work on the browser? If so, I'm not sure this'll be possible since they often need to interact with bazel.

Basic things like syntax highlighting could work though, with other features disabled