Logic Pro X unable to find sound library on external SSD.

Move the Sound Library to an external storage device:

You can store the Sound Library on an external storage device such as an external hard drive or USB drive. You can't share a Sound Library between Mac computers. If you have more than one Mac running Logic Pro or MainStage, each Mac needs its own Sound Library.

1. Make sure you're logged in to your Mac as an administrator.
2. Connect the storage device to your Mac. 
3. If your storage device isn't formatted for use with Mac, use Disk Utililty to format your external storage device as APFS or Mac OS Extended (Journaled).

• • You can't store the Sound Library on a volume used for Time Machine backups. 
  • You can add an APFS volume to the storage device, then use one volume for Time Machine backups and the other for storage of other files.

1. Open Logic Pro, then choose Logic Pro > Sound Library > Relocate Sound Library, or MainStage > Sound Library > Relocate Sound Library.
2. If you are asked to give the app access to files on a removable device, click Allow.
3. In the window, select the storage device or volume where you want to store the Sound Library, then click Relocate. A notification will be displayed when the Sound Library has been moved

If you get an error that says content can't be relocated, give Logic Pro or MainStage access to your external storage device or volume

Important:

Don't rename the storage device or volume after you've moved the Sound Lbrary. If you do, Logic Pro and MainStage won't be able to find the Sound Library.

Wild guess:

With the the computer and the drive off, start the drive, next boot the computer. Start Logic, does it see the library?

Also the library should be the only thing on that partition, did you write to the drive? Put files on the same partition?

Only thing I can think of that may or may not have hapend....... when you plugged or re-plugged the external back into your computer, did it ask you if you want to use it as a Time Machine backup?

Choosing yes, even if by accident, will screw it over for a relocated sound library.

Also, if it was previously used as a Time Machine backup and wasn't fully re-formatted before using as external sound library, again, it won't have it. This may well not be the case, just something to bear in mind.