Here are some potential solutions:
- Ensure that iCloud Photos is turned on. Go to Settings > [your name] > iCloud > Photos, and make sure the "iCloud Photos" toggle is switched on.
- The Faces feature relies on the device's indexing of faces in your photos. It may take some time for the device to analyze and index the faces, especially if you have a large photo library. Connect your device to Wi-Fi and wait for some time to allow the process to complete.
- If the photo was not taken with your iPhone or imported through the Photos app,it might not be part of the library and cannot be edited with features like face recognition.
- Updating to the latest version of iOS might resolve the problem.
See the pic below

If this "Finding People..." is not populating then try to change/edit some of the photos in the People Album from Favorite to Unfavorite and back.
If you are experiencing iCloud syncing issues, sign out of iCloud and sign back in. Go to Settings > [your name] > Sign Out. After signing out, sign back in and check if the issue persists.