From your title and if you're using Cassieopeia, then that sounds like Joomla 4? But I see that you've run Autotune on a 3.10.x site. Asking so that I can try to reproduce it on my appropriate test site.
For the Cassiopeia template, can you try the code change I provided in this thread and see if it resolves the issue? This should fix the dropdown not appearing in J4.
www.sourcecoast.com/forums/sclogin-enhan...n-t-show-on-joomla-4
Also, after the code change, will you re-check the close behavior. When I open the dropdown, I'm able to click out and have it close properly.
-Melissa