Photos App

Hey mstfaltnm

Are you using the same Apple ID across platforms? If so, try restarting your iPhone. Make sure you have a good network connection so updates can sync.

Here's how: Restart your iPhone - Apple Support

Take care.

open www.icloud.com from a web browser , enter Apple ID credentials in photos section , select only an album and click on the photos it can be shared to iPhone via mail Share photos and videos with an iCloud Link on iCloud.com - Apple Support

See a thread Shared Albums not updating on Mac - Apple Community

It will work for iPhone also .