I've checked our records here if there are any related reports and I can't find anything at the moment, Chrissy3.
Generally, when a user encounters unexpected behavior, like UI malfunctions, we can perform basic browser troubleshooting to fix the issue. It could be that the stored cache or an outdated browser is the reason you're unable to view the Category drop-down menu.
We can start by opening a private window and use it to access QBO. You can press Ctrl + Shift + N for Google Chrome or Ctrl + Shift + P for Mozilla Firefox and Microsoft Edge. Once you're in, let's try to add the service item again. If we're able to select a category, we'll have to go back to your regular browser and clear the cache to eliminate the junk files.
If you still encounter the same issue, we can use other supported browsers. It could be that the one you're currently using right now has a temporary problem with QBO. Alternatively, you may check your browser if there's any prompt about upgrading to a new version.
In case you'll need to get helpful insights on the things you buy and sell, and the status of your inventory, we can use your reports to see your sales status.
Let me know how it goes in the comment section, as I want to ensure that you can successfully add categories to your product and service items.