You cannot copy the library to a drive, that is used by Time Machine. And the file system of the drive, where you copy the library to, should also be MacOs Extended (Journaled) and not case-sensitive
I was able to do a Time Machine backup that included the full Photos library on the MacMini. However, I was unable to successfully copy the library itself. I've tried multiple times and always get Error code -36 after approximately half of the library is copied ("The Finder can't complete the operation because some data in "Photos Library" can't be read or written.").
There may be a few items in the library that are having wrong permissions or unreadable path names.
Error -36 means that one of the files cannot be read or written. If reformatting does still not help to copy the library, either use cloning software (super duper, carbon copy cloner) or copy the library by opening the package and copy the folders inside separately.
You could try to isolate the file that is giving this error.
The error -36 could also be created by a corrupted image file or video in your Photos Library.
If the Library cannot be read, and the file system on the destination drive is correct, but you can still not copy, one of the files inside may be corrupted and cannot be read. Then try to copy the library in parts. This way, you are able to identify the culprit that is causing the I/O error and can skip it, when copying:
Create a new folder on your external drive. Call it "Photos Library Copy".
Ctrl-click (or right-click) your current Photos Library and use the command "Show Package Contents". This will open a folder, showing you the files and folders inside your Photos Library.
Copy these folders one-by-one to to the new folder on your external drive. If one of these folders is giving an error -36, check how far the copying proceeded. The files, that have been copied, are o.k. The file or folder, that should have been copied next will be the unreadable file. Probably the problem is caused by one of the files in "Masters" or a database folder. In that case look into the Masters folder and copy as much as you can, while leaving out the file that will not copy.
When you are done, rename the copy of your Photos Library to "Photos Library Copy.photoslibrary" and double click it to open it in Photos. Can Photos open this library?
