I think what they added to iOS 16 only adds the ability for iPhone apps to contribute to the rings.

I’d love to be corrected, but for whatever reason I also can’t get the phone to track steps when my watch is charging, however it seems that if I used a 3rd party fitness app - it would then contribute to ring closures.

I remember older iPhones I could just look at my step count but I can’t get it to contribute without my watch and I don’t have any 3rd party fitness apps.