That does sound like a bug, but just to be sure, also check in the WaniKani settings if Autoplay audio in lessons is active. And in the Self-Study Quiz if the speaker-icon in the top left is yellow. And also make sure that you haven’t muted the browser tab (right click on the tab and see if you can unmute).
The next steps could be to disable your userscript manager (Tampermonkey,…) and test if it changes anything in the lessons, or disable all scripts except for Open Framework and Self-Study Quiz and see if the problem in the quiz is fixed. And/or, after the problem occurs, open the console of your webbrowser (F12 or Ctrl+Shift+I and go to “Console”) and look for error messages (and maybe post a screenshot of it here).