It sounds like your external SSD may not be formatted properly. To avoid damaging the Photos Library an external drive must be formatted in either APFS format (preferred) or in Mac OS Extended (Journaled) format. The drive must be connected directly to the Mac by cable, not networked, clouded, NASed, etc. Additionally, the drive can not have had Time Machine on it since it was formatted. 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.
A Warning: messing around in the Photos Library can corrupt the database. If you want to look around, you should do it with a copy.