Even though WSL shell support has been added to GitHub Desktop as far back as in 2019, the actual option is still missing from the shell list.

There are two ways to enable it:

1) Use GitHub Desktop Beta.

2) If you are using a stable version, you need to enable preview features. Set GITHUB_DESKTOP_PREVIEW_FEATURES environment variable to 1. You can do this in Windows PowerShell:

[Environment]::SetEnvironmentVariable("GITHUB_DESKTOP_PREVIEW_FEATURES", "1", "User")

Restart GitHub Desktop and you should now see WSL in the shell list.