You can however down the extension from the website and install it from the terminal.
codium --install-extension {path to .vsix}
codium --install-extension {path to .vsix}
Microsoft isn't a stranger to distribution restrictions and software usage limitations. I remember uploading Visual C# Express 2010 (freely downloaded from Microsoft's website, without license keys) to a local file sharing website to ease the downloading for my local study group and got a letter from Microsoft's lawyer to take it down.
After that our study group transitioned to Mono with Monodevelop.
1. Install the editor version free from proprietary stuff from big corporation
2. Install a proprietary editor extension by big corporation
3. ?????