I have had this problem too for month. IPhone 12 Mini, IOS 16.3.1 MagSafeCover. I have tried for hours to get NFC working again without success. Apple Pay was working all the time but NFC not. I was using an app to read my German ID card, which was working fine on my IPhone SE 2020 in earlier days, but was not working now on my 12 mini.
Today I tried it again with no success. For testing I am also using the NFC Tools (free version) app from wakdev. I opened the settings page from the NFC app an found a Modus switch there. It was switched to Compatibility in my case. Then I switched it to Normal and for the firtst time since month the NFC reading worked!
I am soo glad that my phone is not broken and i can use the NFC function again!
I hope this can help others too.