How can I sync People, Pets & Places Photos between iPhone and iMac?

My iPhone iOS 17.6.1 has the People, Pets & Places in Photos, but my iMac macOS Ventura 13.7 does not and has a People and a separate Places, but no Pets in the Photos app on the iMac.

I was expecting the iPhone and the iMac to have the same functionality and setup since I also use the same Apple ID so that all the already identified Pets in my iPhone pictures would also be similarly categorized on my iMac. (I know I can go into info in Photos on the iMac and add pets as “people,” but what I want is the the same categorizations on both iPhone and iMac.

Is there some simple selections on the iMac or in Settings somewhere I need to make for the People, Pets & Places to appear?

How does the People, Pets & Places sorting transfer to the iMac supposedly? Does the iMac not have the capability to transfer the iPhones sorting? Do they not share the same sorting even though the photos are synced so my other folders I made myself are identical?

Can I simply get the already found assortments of Pets photos from my iPhone similarly composited in groups to the iMac? (All of the same photos are on both devices, so the iMac has the photos already.)

I want to be able to use my iMac to sort all of the Pet photos so that I can look at them group together by Pet on my iMac, not just on my smaller iPhone. Preferably, the sorting would be identical on both devices.

Thank you for your help.

[Re-Titled by Moderator]