failure to drag and drop my photo library to an external hard drive

no - reformatting totally erases a drive leaving it blank - you either have to move everything to another drive or get a new drive and format it correctly - I personally like Other World Computing for quality products and good customer service with people whoo use and understand Macs

LN

Is your external drive used by Time Machine? Then you cannot drag a Photos Library there. You cannot drag it to any drive with an incompatible file system either. The file system format needs to be MacOS Extended (Journaled) or APFS. And the drive needs to be locally mounted, not a NAS:

This page explains how to prepare a drive for a photos library:

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

assuming causes lot of issues - actually verify that it is correct - Where is it safe to store a Photos Library? Requirements for the external drive

the issues you are having indicates that it is not a proper place

LN

read this article again, more carefully - Where is it safe to store a Photos Library? Requirements for the external drive

The photos library can NOT be on a volume formatted NTFS - it can as the article explains only be on a volume formatted Mac OS extended (journaled) or APFS

the drive needs to be correctly formatted as MacOS Extended (Journaled) or APFS and locally mounted.

LN

Which version of MacOS X are you running on your Mac?

The current version High Sierra is much more strict about the external drives than the previous versions used to be.

Open your external drive in the Finder, and then try, if you can drag your Photos Library directly into an open folder on your external drive. Does that work?

so I feel like it must be compatible.

Please check the file system format, so we can be sure about this. You can see the format, if you select the icon of your external drive in the Finder and then use the key combination ⌘I to open the Info panel.

This line of external drives from OWC are very reliable: OWC Mercury Elite Pro. Pick the one with the size and connectivity you require. Be sure to pick a size with future expansion in mind.

the one that meets your personal needs - as I said I Like OWC - choose one that fits your needs from them or someone else

LN