Solved it. A story with a few twists…
Not a bug in Mail. I restarted in Safe Mode (hold Shift) and the problem went away. Noted what add-ons were running (screenshot of Menu Bar, mainly) and restarted in normal mode. Guess what: The problem was not happening!! I recall that there are times when the problem is there and isn’t. I started Googling for more clues and noticed – wait, the problem is back!! Took another screen shot of the menu bar and compared.
The menu bar when the problem was there had one more icon than the menu bar when the problem is not there. It’s LastPass, which had launched when I fired up Safari. A few tests confirmed LastPass is the culprit. But I have used LastPass for years without issue.
I poked around Lastpass’s settings. It had three Hotkeys set. None of them were [command-’]. But I cleared them all, just because. And the problem went away. Even restoring the settings to what I think they were before could not cause the problem to come back!
My best guess is that the prefs file for LastPass picked up a corruption which was cleared when I manually fiddled with the hot keys.