Speed up yt-dlp self-update detection

[GideonBear]

Checklist

• I have searched the issue tracker for relevant or duplicate issues.

I want to suggest some general feature

See yt-dlp/yt-dlp#15915. This would probably need an addition to yt-dlp itself.

[GideonBear]

Potentially commands can be added to just print yt_dlp.version.VARIANT and other relevant information.