OK, that was helpful. Initially, after downloading the "patcher", there were no instructions on what to do next. Given that it was a "patcher", I was definitely reluctant to double click on the resulting file. But the video guided me correctly. It downloaded Catalina V10.15.1.03, which is (I'm assuming) the most recent, stable, non-beta version. I guess the only other "surprise" is that previously, whenever one downloaded the full OS version, that installation file would wind up inside the Applications folder. In this case, it was in my downloads folder.
I'm going to do a fresh, clean installation of OS 10.15.1, using that installer file, onto my external Samsung 860 EVO 500 gig SSD, and then will migrate/copy needed files, folders, settings, etc. from the internal SSD. I'm hoping that works (I expect it to).
Appreciate your assistance. I still don't understand, though, why I cannot get this installer file directly from the App Store, like I've ALWAYS been able to do. And it's true for both of my Macs running OS 10.14.6.
I had that issue with High Sierra and the App store a long time ago, I just starting using the patcher when I needed the full .app installer. DosDude1 is a legend. Love that guy..