WetGeek I think I'm probably headed for a remove-and-reinstall session.
Yes, but first, thanks to everyone who's helped with this.
I tried removing Vivaldi, but reinstalling it changed nothing. It retained all its configuration, which would normally be a good thing, but in this case the newly-installed Vivaldi was the same as the original Vivaldi. Almost ...
This time the Mail icon did display in the bottom panel, and that brought up a menu from which I could select to Show Mail. That doesn't sound like the most convenient way to display the email client, but it does create a tab for it, which I don't plan on removing normally.
Now, to actually use it a bit, to see how it compares with Thunderbird. Thanks again, everyone.