OK, mucking around I think I've figured out that Avast has recently pretty-radically re-engineered its "Avast Online Security & Privacy (Avast browser security and web reputation plugin)" extension. By default, Firefox settings for add-ons and themes is "Update Add-ons Automatically." (If you know me, you know I detest such things, while granting they are appropriate for most customers.) I had the old (classic) version installed and enabled, and was used to its appearance. So, it "silently" got automatically updated, which changed the extension's visible presentation, including showing the new Avast icon on the menu bar instead of a "shield" icon. This put the new extension in the just-installed-but-not-configured state. It looks like if the new version was actively installed, there would have been some better guidance to help the customer get the configuration steps done.
I think I've adequately gone through the configuration process and will see how that goes.
I've been able to turn off automatic add-on updating; I'm not very comfortable that I will easily know when add-on updates are available (I think I'd have to regularly look at the "Add-ons and themes" pages, which I've not needed to do very often at all).
-dwh