Photos not syncing in Big Sur

They didn't delete the app, they deleted the library. If you have all your photos in iCloud but they are not syncing due to a damaged library then sometimes a solution is to start with a new/clean/empty library.

Please also read the community etiquette guidelines:

https://support.apple.com/en-us/HT208863

If you are logging out of iCloud and back in, you are just slowing down the iCloud syncing, because it will cause a complete new upload of your Photos Library into iCloud.

Can you tell us more about the state of your iCloud Photos Library?

• What is the status bar below the Library > "All Photos" tab showing? Is it showing "Updated just now" or something different?
• Are you seeing an album or folder named "Unable to upload" in the sidebar? If yes, what is inside this album?
• Are you using additional devices with iCloud Photos? Another Mac with a different system version? An iPhone or an iPad? Which system versions are running on your other devices, if any? And what is the state of the iCloud sync?
• In what way does your library no longer sync with iCloud? Do new photos or videos from other devices not appear on yourMac? Do the photos or videos from your Mac not appear in iCloud at www.icloud.com or do they not appear on your other devices? Or are your albums or smart albums not syncing properly?

Are you kidding me, how can deleting the Photos app solve this man? Would you please stop posting here just for the sake of it, you'll give false information to others as well...

The solution to this is to Disable/Enable syncing Photos in your System Preferences > iCloud and then the iCloud sync will be triggered...