We’re using Gitpod for development, and it uses VS Code Browser.
You can’t install directly Plugins from the Microsoft VSCode store. Instead, you need to install the Plugins from the Open VSX Registry. For that to work, the Plugin creator, need to publish their Plugin to this Open source registry.
The publishing seems quite easy: Publishing Extensions · eclipse/openvsx Wiki · GitHub
Github Action: GitHub - HaaLeo/publish-vscode-extension: GitHub action to publish your VS Code Extension to the Open VSX Registry or Visual Studio Marketplace.