Transferring from Photos to External drive

First thing: when someone mentions "external drive," we have to ask (because we've seen this so many times), "How is the external drive formatted?" To get full functionality (and 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.

Move your Photos library to save space on your Mac - Apple Support

Also, by sure to check "ignore ownership" in the Info window for the hard drive.

If that's not the problem, try these things:

• Restart the computer (of course)
• Rebuild your Photos Library by closing Photos and re-launching by option-command-clicking the app icon.
• Make a new user and see if the same problem recurs with it
• 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.
• Start in Safe Mode (different for different computers) This bypasses certain potentially disruptive processes.

           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.

Let us know...

How are you exporting from Photos?

Are you exporting with "File > Export > Export unmodified original" or with "File > Export > Export ... Photos"?

Photos may not be able to export a large batch of photos at once. Can the photos that have been giving the error message, be exported, when you try to export them individually? This will tell you, if some of the photos cannot be exported at all, or batch exporting is the problem.

What is the file system format of the external volume? Does it have a wired connection, or are you accessing it over the network?