Hi
Your photos library is actually a data structure similar to a folder with subfolders. Since Catalina - macos has been a bit remiss in updating the recorded size of the library when it updates the contents. Best way to find the actual space is to right click the libarary - and select "show package contents" (after this be VERY careful not to change any of the contents - or you will likely damage your library). You can then right click on the resources folder and the origninals folder (These two take the vast majority of the space in your library), and click "get info" for each to get a close approximation of the library size (add the two together).
For reference, my 6000 item library takes about 60GB.
When you do get an external drive make sure you get one with plenty of room to grow. It doesn't cost much to get an extra terrabyte or so these days.
Then pay particular attention to the drive preparation - especially the format of the drive, as described:
It must be formatted APFS or MacOS extended (journaled) (preferred for spinning drives)
It Must not be (or have been) used for time machine.
It must have the 'ignore ownership" checkbox ticked.
It should not be on a memory stick, SD or similar.
It stands to reason that if you want any sort of reasonable performance it should be a fast drive with a fast connection.
It must also not be a network drive (a direct connection is required - eg USB or Thunderbolt). File sharing services such as iCloud Drive, Drop box, Onedrive etc are not compatible with Photos libraries.
See
https://support.apple.com/en-gb/HT201517
