How to resolve 'client requested library rebuild' error in Photos after deleting and creating a new library?

Give this a try: boot into Safe Mode according to How to use safe mode on your Mac and try to create a new library. Reboot normally and try again.

NOTE 1: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

NOTE 2: if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode. This makes it act as a wired keyboard as will insure a successful boot into Safe Mode.

I'm not sure, but I think that the first thing I would try is to just delete the Photos Library.photoslibrary file in the Pictures folder. Then, if you double click on Photos, it should create a new Library, free and clear.

If that didn't work, I think I'd create a new Library by closing Photos and then option-clicking on the Photos icon.

If that didn't work, I do the Safe restart that Old Toad suggests. That's always a good thing to try.