Switching this new Library to being your System Library disconnects any other Library from iCloud. Only the one System Library can be connected to iCloud.
But first, how is your SSD drive formatted? To avoid damaging the Photos Library an external drive must be formatted in either APFS format or Mac OS Extended (Journaled) format. 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 the format is not properly formatted, then you should immediately stop running the Library on that drive.
If the format is OK, then you can open the Library by double clicking on it. Then, in Photos' Settings>General, make sure that the Library is designated the "System Library"

Here, "Use as Photos System Library" is grayed out, because it already is.
Then you need to connect the Library to iCloud in Settings>iCloud
