As I continue to learn ...
KDE Connect actually consists of two applications that I've found so far. They show up in the Internet menu as KDE Connect and KDE Connect SMS.
These can be run concurrently, as shown above
The other thing I confirmed is that KDE Connect isn't limited to running only on the Plasma desktop. In the list of available devices for pairing you see above, you may notice that one of those defices is named server-solus-4-3-budgie. Indeed I can connect my laptop to the machine that's serving Solus torrents just by virtue of their being on the same network and both running KDE Connect.
At this time I'd like to thank @tomscharbach for reawakening my interest in cross-platform communication. RDP was a way of life for me when I was working as a software engineer, but this goes much father than RDP.
I now have my phone, several tablets, and various computers talking and sharing resources with each other, and I'm now thinking of things I'll now be able to do easily. Most of those are things I didn't realize I wanted to do until now.
The next adventure: finding out if KDE Connect is available on my Ultramarine Budgie laptop.