When trying to use the "Allowed Product Categories" setting of the coupons it does not suggest any of the categories and that option is therefore not usable.Using Joomla! 3.9.22 and VirtueMart 3.8.4 10335.
works fine here so you need to investigate your category select call -- JS errors etc
It is a language specific SQL query bug in VM 3.8.4. The error is generated if your site uses any language other English - GB.
Update VirtueMart latest 3.8.6. That will resolve the issue.