I’m not aware of any official YouTube Music Desktop application on Github, YouTube Music is a music streaming service provided by Google, it allows users to access music videos, albums, and playlists on the YouTube platform.
However, you can find some open-source projects on Github that allows you to play YouTube Music on a desktop, these projects are created by independent developers and they’re not officially supported by YouTube or Google.
These projects are based on the YouTube Music Web player, they provide a way to access YouTube Music on a desktop using a web-browser and some of them even provide additional features like desktop notifications, media keys support, and more.
It’s worth noting that these projects are not officially supported by YouTube or Google and they may have some limitations or bugs. They also may not be working properly due to updates on the YouTube Music Web player or changes on YouTube’s terms of service.
You should also check the project’s documentation, and the Github repository for more information about the project, and also check the project’s last commit date, it might be an indication of how active the project is.