Photos app stuck updating from iCloud library

How large is your Photos Library in iCloud?

If it is large, the updating may take several days. Then do not interrupt it. If you disable the iCloud option and turn it on again, the updating will start over from scratch.

There are three common reasons for iCloud not syncing after the Mojave or Catalina upgrade:

• The network connection: iCloud Photos needs a Wi-Fi connection, not a cellular hotspot. Are you connected to Wi-Fi? Also, a Firewall could be blocking the connection to Apple's cloud servers. If you are using a third-party Firewall or Antivirus filter, like Kaperski or Little Snitch, disable it.
• The location of your Photos Library: The library must not be on an external volume, that is used for Time Machine backups or is having any backup software installed. It needs to be locally mounted, not accessed over the network. Even if it worked with a previous system version, it will no longer work withCatalina because of the new security features.
• Media files in an unsupported format. The iCloud sync can get stuck, if your Photos Library contains PDF files or older image files or videos, in a format, that QuickTime Player can no longer open.

If you still have your old Mac, check your Photos library there for legacy media and convert them to a different format, that will work on catalina. Here is a checklist for iMovie: About incompatible media in iMovie for macOS - Apple Support. Items that are safe to use in iMovie should also work in Photos.