Having been stopping Mail Shield "until your next restart" the first time that I failed to send or receive e-mail after every restart for over a month, today I finally found after a restart that Thunderbird/gmail/Avast were happily working together again at last. I presume that, since my previous restart, somebody at gmail or at Avast (or even at Thunderbird) changed something that had been broken. In Thunderbird, Help: About: still reports "78.4.0 (32-bit)", so that does not appear to be where the fix has taken place.
Thanks for all the suggestions and advice.
You're welcome. (Side note, the latest version of TB is 78.5.1)