You don't mention which iOS version you're running on that phone. The compatibility page about the app mentions that you need:
minimum iOS version 15.0 (Face ID available from iPhone X)
Note: iOS beta versions are not supported.
If you've got an old version or a beta version, you may encounter problems I guess. Although another option is that the NFC reader in your phone is somehow not working well. Have you tried restarting the phone? Switch it off (completely) and restart. Sometimes that helps to get misbehaving bits of hardware working again. The NFC function should always be on for an iPhone. I do not know how to test it other than with another NFC tag I'm afraid.