OK, so, after hours and hours over a couple of weeks on the phone with Apple Support (Jasmine, you never lost patience and followed through with every task and promise, thank you!), it appears that the problem is resolved. Fingers crossed!
Apple support tried everything, including creating a new user account, checked the date and time, safe boot, reset of my network, hard reset of my network; I cannot remember it all, but nothing worked. At one point, Apple thought it was Catalina; at another point, Apple thought it was my network, and back and forth. (My ISP was not having any of it, telling me that they have been inundated with complaints about Apple and that it was Apple's problem... nice. Too bad for me they have no equal competition where I live.
Bottom line, even though we previously tried a hard reboot of my network (modem) several times, today, while working on my Mac, with several apps open (I don't recall if the App Store app was open or not), my power went out. It was out for 30-45 minutes, but seemed like hours. When the power came back on, I restored my computer windows, and just for fun, tried to log into my account in the App Store... it works! Again, fingers crossed! It has been working and allowing me to download apps for several hours, so, to this novice, it appears that it was my ISP. It appears that the forced hard reboot worked. Apple Support says it may have been caused by a strengthening of security within Catalina that caused the login problems.
IDK, but if you are having the same problem, I recommend trying a hard reboot several times before wasting weeks trying to resolve the problem by other means. Perhaps leave the modem down and without power for an extended period of time. I am not a techie, but hope that this may help someone avoid the frustration I have been experiencing.
