Getting “Unable to Check for Update” error when trying to update to iOS 13.1
You have done everything that you can do from your iPhone. The solution for you at the moment is to use iTunes from your Mac/PC if you really want to have iOS 13.1.

If you want to update immediately, plug in your iPhone to your Mac
Update via iTunes by clicking the Check for Software Update button


I got the same issue and with iTunes, I was able to fix it. Sorry, at the moment with my knowledge those basic solutions from the phone don't work and didn't help me. I would love to hear if anyone has fixed via iPhone only.