How does Time Machine treat changes to the Photos Library? 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?
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:


Edited since the last backup is backed up again in the next backup
Created since the last backup is backed up in the next backup
Deleted since the last backup is not included in the next backup (i.e. there is no record of it in that backup, but the file itself is still stored for any older backups it was a part of)


Now, the confusion usually comes from the way Time Machine actually does a backup. I'll try and explain this below.


The initial backup TM does on a new backup drive is a full backup of
your Mac. So, if your Mac has used 80GB of a 1TB drive, then the 
first backup will take up 80GB of space on the new backup drive.
All remaining incremental backups do not do a full backup. Instead TM backs up any new data (i.e. newly added data and any edited data) and keeps a record of any deleted data.
In the case of files such as Packages (including the Photos Library package), TM will identify any:


new data (e.g. new photos in the Masters folder within your Photos Library package) and back this up
modified data within your Photos Library package (e.g. edited photos) and back this up
deleted data within your Photos Library package (e.g. photos you've deleted) and keep a record of the change

When the backup drive runs out of space, TM will delete as many of the oldest backups it needs to in order to be able to do the next backup (and this is where users can lose data that was not part of more recent backups)
Regardless of whether it is the initial full backup or an incremental backup, TM will display this to the user as if they're all separate full backups. This is designed on the basis of User Experience (UX) design so that it's easier for users to browse and find data, and acts to reassure users that it's all there. According to Apple:



  ...what makes Time Machine different from other backup applications is
  that it not only keeps a spare copy of every file, it remembers how
  your system looked on any given day—so you can revisit your Mac as it
  appeared in the past.


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.