It’s actually better the way it is. If someone has access to write, then they’ll see the categories and be able to choose the right one. Once there’s a post, the category will show up.
If you show a ton of empty categories, how many clicks do you think it will take before people give up and leave your site? A menu with a bunch of fake entries pretty much defeats its own purpose.
If you really want to go that route, then you could probably make one pointless post and check all categories when you publish it. That should probably make them all show up. But when you add new categories, you’d have to go back and edit the post to include them.
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