photo stream does not update on mac

It's been discontinued for new Apple ID accounts only per this Apple document; Get help with My Photo Stream - Apple Support

The following is from that document:

* If you recently created your Apple ID, My Photo Stream might not be available. Use iCloud Photos to keep your photos and videos in iCloud.

That’s only half the story. My Apple ID is 15 years old,but photo stream is not working on macOS only on iOS. Same on other customers that I look after. As far as I see Apple is quietly phasing out photo stream,but doesn’t say so officially

Are you receiving an error message? What exactly is or is not happening? I would recommend you use this article to help troubleshoot the issue Get help with My Photo Stream

same here. My research comes to the conclusion that Photo Stream on MacOS is discontinued by Apple, though they don't say it.

Sadly that is a problem with Apple. Sometimes it helps to uncheck and check again photo stream on the macOS devices, but this is not a permanent solution.