updating photo library takes too long from external hard drive

How is your external drive formatted? To avoid damaging the Photos Library an external drive must be formatted in either APFS format or Mac OS Extended (Journaled) format. 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 this drive is in a an incompatible format, stop running Photos with it immediately!  A Photos Library can sit on an incompatible drive, but running it may corrupt the database.

In addition to the format of the drive is it an HDD or SSD?

If an HDD is it a 5400 rpm model or a 7200 rpm model?

How much free spade do you have on the drive?

Does the drive have its own power source?

Have you installed and run any "cleaning", "optimizing", "speed-up", anti-virus or VPN apps on your Mac?