I did some more snooping as I was experiencing this on our development server, but not our live server, both running Moodle 3.5.
In the end, it was the HTML Tidy filter that was causing the issue, although it is installed in both places. I clearly have some more snooping to do, but to troubleshoot the issue, disable all filters on a lesson, see if it works correctly, then selectively re-enable each filter one at a time.