YouTube Discontinuing Support for Safari?

I'm not sure it's ever been listed on https://www.youtube.com/supported_browsers but it is on https://support.google.com/youtube/answer/78358?hl=en and https://support.google.com/youtube/answer/175292?hl=en

There's not a lot to extrapolate from this without knowing exactly what version of Safari/macOS you're on.

Version 13.1 (15609.1.20.111.8)

Your macOS is out of date, update to latest.