The post "Sep 16, 2020 11:52 PM in response to plaidflannel" from Urquhart1244 DID solve my problem.
After using the Amazon Fire TV Stick for several months, I am finding the interface to the Apple TV to be more difficult to navigate. A Google search for information on how to install CBS AllAccess on the Apple TV said to look for the App Store in the top menu bar. I interpreted that as meaning a row of text links at the top of the screen. It turns out that the App Store icon was several rows down (and off the screen) in the colorful rectangles.
My second error was that I was trying to find "CBS AllAccess". In the App Store, there was only "CBS Interactive". After installing that app, I was able to use the login credentials for my existing CBS AllAccess account. A cursory examination suggests that all of the programming in "CBS AllAccess" on my Fire TV Stick is also available in "CBS Interactive" on the Apple TV.
Thanks to Urquhart1244 for the detailed help.
Now all I need to do is find a user-friendly third-part remote control for the Apple TV to replace the clumsy one that came with the device.