The System Library can be on an external drive. To get full functionality (and to avoid damaging the Photos Library) an external drive must be formatted in either APFS format or Mac OS Extended (Journaled) format. Additionally, the drive can not have had Time Machine on it since it was formatted.
Move your Photos library to save space on your Mac - Apple Support
The Photos Library keeps the full resolution, absolutely original images. The edited copies are not separate files-- the edited version is created for you to look at and work on from the original plot the instructions about what changes you made. The originals are never messed with. Even the metadata remains unchanged.
If you use iCloud and select "Optimize Mac Storage," then the Mac may keep only low resolution images, and the full originals are stored on iCloud to be retrieved when needed. If you use iCloud and select "Download Originals," then the Mac will keep the full sized Originals. When you make backups, is should be after Photos has downloaded the originals.
If you keep your System Library on an external drive, and it's connected to iCloud, then the drive needs to stay plugged in to allow Photos operations that occur in the background even when Photos isn't running. Otherwise Photos gets confused and may have to spend a lot of time re-syncing. You may be able to disconnect from iCloud and unplug the external drive without upsetting Photos. I'm doing that some, but not with a significant library, so I'm not so sure about that.
