on a 600Gb hard drive
The migration will try to create the migrated library on the hard drive, if the file system is supported. How is this drive formatted?
If the drive is not directly connected, or the file system is not MacOS Extended (Journaled), or the drive is a backup drive with Time Machine or WD Smartware or similar, then the library cannot be migrated on that drive. Photos will create the migrated library on your System drive.
Move the library to a different drive formatted MacOS Extended (Journaled).
If you are getting error messages about "Not enough Space" when trying to migrate a 2,2 GB Library you are probably running out of storage on your system drive. How much free storage do you have?