Restoring Photos library from Time Machine

EricWeir wrote:

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My library is synced with iCloud Photos. I take you to be saying that there could be a discrepancy between my iCloud Photos and the Time Machine backup of the Photos library.

Yes. Time Machine can only backup the items that have been downloaded from iCloud and are mirrored locally on your Mac. So the Time Machine backup may have missing originals, if the syncing has not been complete, when the particular backup has been made, or if you have enabled the option"optimize Mac Storage".

I don't understand making the restored library the iCloud Photos library and then syncing it with iCloud. Would not doing the former be doing the latter? And how does making the restored library the iCloud library resolve the discrepancy?

After you restore an iCloud library from Time Machine, your previous Photos Library will still be the System Photos Library. When you open the restored library in Photos you have to make it the system Photos Library in the Photos > Settings > General tab, and then enable iCloud Photos in the Photos > Settings > iCloud tab. Then should Photos be able to download incomplete item from iCloud, but only, if they have not been deleted from iCloud. The video you accidentally deleted from Photos will also have been deleted from iCloud. If it had not yet beed downloaded from iCloud when the backup has been made, the Time Machine backup may not include the original and you may need to go back further in time.

in addition to Richard's advice on the restoring - did you restore the library from the Time Machine backup to the same folder where your library originally has been or did you restore it to some external drive? If the library is on an external drive, the file system format should be compatible with Photos, either APFS or MacOS Extended (Journaled) and not case-sensitive. With a different format, the internal links in the library might not be restored properly and Photos may not be able to find the video components in the container formats like MOV or HEIC.

If your library has been syncing with iCloud Photos the Time Machine backup may be incomplete and some originals missing. In that case you have to make the restored library your iCloud Photos library and sync it with iCloud before all originals will be available.

How did you "restore" the Photos Library? You can't just drag a Photos Library from the data folder, but you must use Time Machine's "Restore" routine:

If you use Finder to open Time Machine, you should see

an Enter Time Machine button at the upper right, or

there's the Time Machine icon on the Menu bar.

Time Machine does incremental backups, so a particular dated file won't have all the information. You need the Time Machine app to put it all back together.

Does this work?

EricWeir wrote:…If I had elected to overwrite the current copy I would like to think that the videos could be played, exported, etc. And I still have my question: if I make the restored copy the current copy that be the case?

Photos has no way to know what current copy and restored copy mean. You can double click on either one and see what's there. You can use File>Import to bring in pictures and videos from another Library.

Whichever you decide to keep, make it the System Library in Photos' System Settings>General. The System Library is the only one that will work with other apps like Safari, and it's the only one that can connect to iCloud Photos.