Photos does not have the necessary permissions to create a library in the folder that you selected I'm attempting to create a new macOS Photos.app library on a secondary hard drive.
In the Choose Library window, when I select Create New... and select the external HDD, I get the error:

The library could not be created.
Photos does not have the necessary permissions to create a library in the folder that you selected.


Why can't I use the external hard drive for my Mac Photos Library?
My external HDD was in the HFS+ file format. The system's boot SSD was using the newer APFS.
I used Disk Utility to reformat the disk as APFS.
After switching to APFS I re-created the new Photos library and it worked fine.

We can move our Photos Libraries to an external drive, but the drive needs to be correctly formatted as MacOS Extended (Journaled) or APFS and locally mounted.

Pre-APFS file systems should work, but for some reason it wasn't working. Perhaps related to permissions, or the the file system itself. Switching to APFS fixed it for me.

I found a great resource for this question here:

Where is it safe to store a Photos Library? Requirements for the location of a Photos Library - 2019 version
https://discussions.apple.com/docs/DOC-250000663