Thanks for the details--I get it now! All the memory stuff looks fine-- you should not let the "used" get more than 90% of the total.
But I don't have an answer. I "favorite" (a verb?) pictures in Photos on my Mac, and they are immediately (well, that depends on wifi, etc) favorited on my iPhone and at iCloud.com. And it's just as fast the other way-- I just made sure.
So, since iCloud Photos agrees with your Mac, it must be that the iPhone is the weak link. Does favoriting transfer from Mac to iPhone for you?
The "attributes" transfer separately from the pictures, so changes in captions, favorites, etc. may take longer to happen.
On your phone, check in the Collections > ID icon
to see if syncing is paused. Keep in mind that iCloud is designed primarily for mobile devices, and since syncing uses the battery, and since lots of people are very anxious about battery drain, the iPhone will avoid syncing when not plugged in. And since syncing uses processing power, and people hate slow-downs, the iPhone will avoid syncing while you are using it. And since syncing requires bandwidth, the iPhone will avoid syncing when the internet connection is weak.
So, if you want faster syncing, then find good wifi, plug the phone in, and leave it alone.