Can't add a new card to an empty wallet

I had one credit card in my iPhone wallet, and today I reset the network settings on my phone (for unrelated reasons) and the credit card disappeared from my wallet. And when I try to add a new one, I get a message saying "Unable to Add Another Card: You have added the maximum of 8 cards for Apple Pay. You can remove one of your current cards to add a new one."

However, there are no cards in my wallet to remove. I've restarted the phone, run the latest iOS update, restarted the phone again, tried accessing my wallet directly through the app and also through the settings page... and nowhere can I find these supposed 8 cards in my wallet to remove. I've googled the problem and found a similar question here in the communities but it was old and never resolved.

I'm on an iPhone 6s with iOS 12.2.

Any suggestions?