I've searched all over and can't find a sure answer to this question. If a new photo is added to my iCloud Photo Library, resulting in a change to the "Photos Library" package on my Mac found in ~/Pictures, does Time Machine simply back up the delta within the package or will it store another copy of the entire library?
Mac – How does Time Machine treat changes to the Photos Library
photos.apptime-machine
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Best Answer
SHORT ANSWER
Time Machine only backs up new or modified data, and keeps a record of any deleted data. This includes what's in your Photos Library. It does not do a fresh backup of the entire Photos Library each time you make changes to it.
LONG ANSWER
The way Time Machine works is that it backs up anything that has changed since the last backup. For example, a file that is:
Now, the confusion usually comes from the way Time Machine actually does a backup. I'll try and explain this below.
Source: Mac Basics: Time Machine (web archive of Apple knowledge base doc)
Finally, as added reassurance that TM does not do a full backup of your Photos Library each time, I can share a personal example. My family Photos Library is 341GB in size and if this was fully backed up each time then the 2TB external drive that it's backed up to would be full after only 4 or 5 backups (allowing for other data), but that particular TM backup drive has backups going back to late 2015.