Sounds like that is the best next step. Better to have Apple have a look at the phone and determine if everything works as advertised. From the experiences you describe, it sounds like the NFC reader is not doing its job.
I have used a similar app on my phone and on my partner's phone to scan ID documents for a couple of identification purposes, in my experience it is actually a very easy to use system. Once set up, you will not need to scan your passport again. A shame that you are running into all of these issues!