I just pushed an update to this component.
https://github.com/discourse/discourse-header-submenus/commit/cbb1c280f031024335cf3b103b0e2c242c5862b1
There are no visual changes and if you’ve added custom CSS to your theme, it should still work because the component still has the same classes.
I dropped the external library that the component previously used and jQuery by extension. I went through the issues reported here, fixed the one I could reproduce and then deleted the replies to keep everything tidy. If your problem still persists after the update, please feel free to post it.
Beyond that, the update only adds one new feature. The submenus will now show on hover on desktop instead of requiring a click.