copying photos library to external HD
How do I copy my full Photos library to a WD My Passport 4TB external hard drive
iMac 21.5″, macOS 11.7
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If you're using iCloud to sync your devices, then you can just set up a new empty Library on the hard drive, designate it as the System Library (in Photo>Settings) and then wait for iCloud Photos to download to the new library. Be very patient-- it could take days or weeks, depending on the size of the Library.
If you're not using iCloud, you can just drag your Library to the hard drive-- then double click on it. To get full functionality (and to avoid damaging the Photos Library) an external drive must be formatted in either APFS format or Mac OS Extended (Journaled) format. Additionally, the volume can not have had Time Machine on it since it was formatted. See this:
Move your Photos library to save space on your Mac - Apple Support