Export from Photos

Can you tell us more about what you're doing? For instance, are you using File>Export>Export Original, or something different? Do you use iCloud to sync Photos on your devices? Do you have "Optimize Storage" checked? Can you export pictures to a folder on your internal drive? If so, can you move that folder to the external drive?

Have you tried moving the entire Photos Library to the external drive, and changing the name? Then you would have two independent libraries, and deleting pictures on your internal drive would not affect the library on the external drive.

How is your external drive formatted? To get full functionality (and to avoid damaging a 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

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What system and Photos versions are you using?

It is all photos or just the one in the screenshot?

What is the extension of the file in the screenshot?

How is the drive you're exporting to formatted and connected to your MBP?

Are you trying to export the unmodified original or an edited version?

Yes, make sure to delete all images in the Photos Library via the Photos interface. If you just delete images from the library via the finder, Photos will get confused and corrupt the library.

Images deleted in Photos will hang around a while to give you a chance to change your mind. Eventually, they will be permanently deleted.

Delete photos or recover deleted ones in Photos on Mac - Apple Support

It sounds like you now have moved your Library to the external drive, so you now have a Photos Library on your external drive and you also have one in your Pictures folder on your Mac. You can switch Photos back and forth between them. One way is to Option-Click on Photos (when Photos is closed) and you will see a list of Libraries, so you can click on the one you want. Or, maybe easier, you can double click on the Library file on the external drive and it will open in Photos. (Double click on the internal drive library to go back to it.)

So if you open the external drive library, you can look at your pictures and make sure they are all there. Once you're sure about your pictures, you can delete the ones in the internal drive library. As Keith Barkley said, the the deleted pictures go in the "Recently Deleted" album where they stay for 30 days. If, after waiting a few days and satisfying yourself all is cool, you can force the recently deleted pictures to be permanently trashed.

Permanently means just that! Pictures are precious, and you should have another copy of that library on a completely different drive--just in case!

That means those libraries don't have deleted items. Why can't you open your main library?

If it is on your computer, you can launch Photos with the option key held down and browse to it.