Photos (Macintosh running Big Sur) and iCloud

I have designated a new Photos library to be my Photos System library. I'm now trying to get iCloud to synchronize with this new library. Specifically, I want the photographs stored on iCloud to download to the Mac's Photo library, which I've selected in Photo's Preferences to be the Photo's system library. (This library is on an external drive connected to my MacBook.)

However, iCloud doesn't appear to be synchronizing. I can see that iCloud now sees a couple of new albums that were on the Mac, but hasn't uploaded the photos into those albums. Nor has iCloud downloaded any of the photos on iCloud into the new Mac Photos system library.

How do I get iCloud to synchronize these two libraries so that I have all my photos on my ?

Cheers