Hi macaston22,
Welcome to the Apple Support Communities.
From your post, it appears that you have an issue with a missing third-party app, Private Photo Vault, after restoring your iPhone from an iCloud backup. You have reviewed the Which iCloud.com features are available in the browser on your device resource. We want to help.
You can follow the steps in this article that talks About missing information after you restore your iPhone, iPad, or iPod touch with iCloud Backup
From this resource you will see that "For some third-party apps, you may need to download data from the app provider again."
Hope that helps.
Have a great day!