Just to be sure, In Photos>Preferences>iCloud is "iCloud Photos" un-checked? How about Photos>Preferences>General>Importing-- have you checked "Copy Items?"
If both are "yes," it may be that the Photos database has lost some connections. Try rebuilding your Photos Library by closing Photos and then command-option-clicking the Photos icon. This will bring up a dialog (sometimes hidden behind other windows) offering to repair the Library. It will take a few minutes.
Or you could try making a new user to see if the same problem recurs with it.
Or use another library if you have one, or make a small test Library with a few pictures in it and see if the same thing happens.
You should try re-starting your computer in Safe Mode. This bypasses certain potentially disruptive processes. Safe Mode is different for different computers, so see this:
Start up your Mac in safe mode - Apple Support
The idea is to find out if the problem is with the Library, with your account, or with caches and login items, and stuff like that. One of these steps may fix the problem, but their failure to work is also diagnostic.