Cannot find the System Photo Library

Check the trash. I don't know why, but sometimes (probably an errant swipe) Libraries end up in the Trash. A Photos Library will work nearly everywhere except in the Trash or in iCloud Drive, so check there, too. When you find it, move it back to the Pictures folder, and double click it.

Since the Photos Library is the only thing with an extension of ".photoslibrary" you can search for that--I'd use the Finder search

Another thing to try is to close Photos and then option-click the Photos icon. This will give a list of every Library that Photos knows about. But, of course, if it knows where the Library is, it wouldn't give the error message. But it's worth a try.

By the way, did you have any pictures in Photos?

Let us know what you find and if you need more ideas…

Make sure that photos is having access to all your folders by system settings>privacy>Click files and folders>make sure photos is added to this list

You can also try and find your photos library here: Homefolder>pictures

Launch Photos with the Option key held down and you will get this window which, if there is one, will show which is the System Photos Library:

If it doesn't show up then you do not have a System Photo Library and will have to assign one.