Drag and drop works for me as well, but be careful-- you can never be sure what you will get-- the original, the edited version, a thumbnail, a preview size? And it changes from OS to OS. So check first that you get what you want! Of course, you're not getting anything at all…
Where is your Library located-- in the Pictures folder, or is it on an external drive? I'm asking because, 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. There have been so many problems with using incompatible drives that the newest macOSs won't even allow a Library on a non-Mac formatted drive to open, since there is a chance of damaging the Photos database. See this:
Move your Photos library to save space on your Mac - Apple Support
You're not using the newest OSs, so the problems may be more subtle. If the Library is on an external drive that is not properly formatted, you should stop using it.
If the drive is fine, but you can't get drag & drop to work, then to narrow things down, try these steps:
- Restart the computer (of course)
- Re-start in Safe Mode. This bypasses certain potentially disruptive processes, and it often helps. Safe Mode is different for different computers, so see this:
Start up your Mac in safe mode - Apple Support
Those are the easiest things to try first. Then try these:
- 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 can create a new Library by closing Photos and then option-clicking on the Photos icon
- Make a new user and see if the same problem recurs with it
- Rebuild your Photos Library--close Photos and re-launch by option-command-clicking the app icon.
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 also helps figure out what's happening.
Let us know what happens…