OK - I am a long time Lightroom Classic user and have not really used the new Lightroom very much.
I have a pretty typical workflow, I think, namely:
1. I have a desktop computer at home that houses my main Lightroom catalog. This is where I keep all my 400k+ photos.
2. I also have a laptop for use on the road. I have Lightroom Classic on this device as well, and since it is a different computer than my home machine, it is therefore a different Lightroom catalog (much smaller that sits on my laptop).
I do mostly sports photography and typically after a game I will import everything from that game to my laptop into Lightroom Classic, and then when I get home I import the same photos from the same SD card to my desktop machine. Needless to say it would be great to import only once to the laptop and then have those photos sync'd to my desktop automatically, along with any adjustments I make on the laptop before I get home.
The problem appears to be that I can only 'sync' one catalog to the Adobe Cloud at a time, so when I create a sync'd collection from one machine, the other one isn't able to see it.
I have a feeling that I am doing something wrong here and missing the big picture, I'm just not sure what it is.
You are not doing anything wrong. That is the way it is: you can only sync one catalog to the cloud, so you cannot use cloud sync to sync Lightroom Classic catalogs on two computers. What you can do is install Lightroom desktop on the laptop (too). That would give you access to the synced images from the laptop.
I use the cloud version of Lightroom on a limited basis. Using it I can take photos with my iPhone using the Lightroom camera and when I returned to my desktop computer using Lightroom Classic the images that I took are already downloaded to Classic and I can work with them on my desktop computer. Also, if I import any images from my digital SLR directly to Lightroom (For the cloud) they will automatically sync with Lightroom Classic on my desktop. Don't know if either of those features are anything you need. But that is how I use the "new" Lightroom.