We are paid members of Discourse. I accidentally deleted a category, and since this is our first time using the platform, we didn’t make a backup beforehand. Is there any way to restore that category? Alternatively, if I can create a new category with the same URL slug as the original one, that would also work — because we have an app that embeds the link to that category.
Could you please advise how we can proceed?
You can email team@discourse.org in this case (though the community is also good to help), but I think they usually don’t work on weekends.
You can’t delete a category if you don’t delete the topics in it beforehand.
Either you deleted an empty category, in which case you can just re-create it, or you actually deleted the content before this, in which case you need help from the Discourse team and see if they can restore the lost content.
Edit: I’m not sure you can restore a deleted category with the same ID, tho 
Yeah, probably not: Recover deleted categories - #4 by pfaffman
So you just deleted an empty one? Just make a new one with the same name
The new one will have a new category id, which is the only part of the url that matters.
It week be easier to uodate whatever is writing to discourse.