Hi - iCloud does not normally require more space.
Have you used iCloud photos in the past, on this or any other device? Ie Is it possible you have previously stored images there that have now been merged with your library?
If the sync is still going on, it is possible that the library will grow while it is syncing, but that should be temporary.
And I understand from your post that you have the library on an external drive. If so, is it correctly formatted (an incompatible format for a drive can cause all sorts of strange behaviours with a photos library). Normally when you buy a new drive it will be formatted ExFAT (a microsoft format) which is not compatible with a photos library, and needs to be reformatted on the mac first.
It must be formatted APFS or MacOS extended (journaled) (preferred for spinning drives)
It Must not be (or have been) used for time machine. (A time machine drive can be used if re-formatted first)
It must have the 'ignore ownership" checkbox ticked.
It should not be on a memory stick, SD or similar.
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.
It stands to reason that if you want any sort of reasonable performance it should be a fast drive with a fast connection.
See
https://support.apple.com/en-gb/HT201517