Unable to view photos library moved to external drive on my MacBook Air

It looks like your external hard drive might not be formatted for Mac. To avoid damaging the Photos Library an external drive must be formatted in either APFS format or Mac OS Extended (Journaled) format. 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

If this drive is in a an incompatible format, stop running Photos with it immediately!  A Photos Library can sit on an incompatible drive, but running it may corrupt the database.

Now, in addition to that really big thing (!) can you tell us about your iCloud Photos use? Are all your pictures synchronized to iCloud Photos at iCloud.com? Are you using "Optimize Storage" for Photos? Is a Library still in Pictures on your internal drive?

If all the pictures are at iCloud.com, then here's what I would do: I'd format that drive with APFS using the Disk Utility app. Then I'd create a brand new empty Photos Library on the new drive. (Close Photos; option -click on the Photos Icon; choose "Create.") Then I'd designate the new Library as the System Library, and I'd turn on iCloud with Download Originals. Then I'd wait a week or two as that Library filled with and scanned all the pictures from iCloud.

What do you think?

Wet Baloney wrote:

1) The external drive is formatted as APFS

2) My photos are synchronized to iCloud (3devices - iPad Pro, iPad mini, iPhone). I think they were on the MacBook Air before all this but now I get this: [System Library]

3) No, I deleted the photos library on my internal drive.

Would I be able to regain access to the photos library on my Mac if I just put it back where it was in the first place?

All that helps, but you did not answer "Are you using "Optimize Storage" for Photos?" That is the cause for the part about erasing pictures that are not fully downloaded. If you are not using "Optimize," then you don't have any of those. In either case, the full original files will remain at iCloud.,com.

A Mac can have several Photos Libraries, but there is only one System Library, and that's the one that is used when apps access Photos. It's also the only one that can connect to iCloud. If you want to use the external drive Library for with iCloud, then you need to designate that it's the System Library at Photos' Settings>General, and you need to connect to iCloud at Photos' Settings>iCloud.

You ought to first make a backup of your Library! You can just copy it and paste it in another folder, but it would be better to use another drive.

By the way-- as to "I deleted the photos library on my internal drive." -- deleting something before you know that everything works is a bad idea.

I read that message as saying that the old copy of your library (on your internal drive) will be disconnected from iCloud Photos Library, and then you must turn it on for the copy you created on the external drive.

Be sure that the external drive is an appropriate format first, as Richard.Taylor pointed out, of course.