I have ported your extension to GNOME 45, but with some modifications

[KSXGitHub]

The code is here: https://github.com/KSXGitHub/gnome-shell-extension-github-notifications

I have replace the code that makes HTTP requests to GitHub with Rust because libsoup3's API for this was just too complicated.

Feel free to merge it and convert it back to using libsoup3. I prefer not having to maintain too many things.