"Syncing Photos" without a number - what does it mean?

[Tangible]

Apologies in advance if this is already dealt with; a search didn't turn up anything relevant.

I'm in the process of migrating about 25,000 items to the cloud, and have checked the box to keep a copy of everything on local storage. For about three days, when I clicked on the cloud icon in the upper right I would see a countdown, starting from 25,000, at a rate of 2 or 3 seconds per image. Some time during the night it finally reached zero.

Now I see just the words "Syncing Photos", with an animated blue circle but no numbers.  What exactly does this mean? Is LR now downloading the photos to my hard drive? Can I use the program while this is happening, e.g. import new photos from my camera? Can I now set up LR on another computer? Since there's no countdown, is there any way to predict how long this process will take?

[Tangible]

Some additional data:

The file on my Mac named Lightroom Library.lrlibrary shows a "get info" size of 382GB, which is roughly the size of all my items. The containing folder, Lightroom CC Saved Photos, shows a size of zero. That doesn't make much sense to me, but perhaps someone can explain what's happening.