I figured out what the problem was. It was the bozo on the keyboard (i.e., me) not understanding how WordPress operated and how its configuration settings interact.
The first problem was simple. When I created a new “latest posts” page (in Elementor) it was displaying the list of blog posts…but because I didn’t update the link setting in the menu item for ‘Blog’ I never saw it. Instead, clicking Blog in the menu dutifully took me to the previously-used latest posts page…which because it wasn’t set in Settings -> Reading Settings as the latest posts page displayed nothing. As it should have. Updating the menu link for Blog — so it pointed at my new latest posts page — solved the problem.
Along the way I also noticed that the Elementor styling was being ignored when the new page was displayed. That was caused because I had set the page to be an “official” latest posts page in Reading Settings. Which overrode all the content in the custom page, replacing it with a default list of posts. The solution to this was to leave the “latest posts” page undefined in Reading Settings and use Elementor widgets to add the latest posts list to the new custom page.
Leaving that “latest posts” setting undefined results in a warning (which isn’t terribly clear). But it appears to be a warning you can safely ignore.