As you can see in my comment to your question, we faced a similar issue where the NFCNDEFReaderSessionDelegate was not being called. To resolve this we needed to change our implementation to NFCTagReaderSessionDelegate and specify the polling option for iso15693 tag type. Once implemented this way, the write functionality worked as expected. I've no idea why this behaviour changed between iOS versions but hope this is helpful.

Hi. In relation to this we have recently discovered that writing to iso15693 tags seems not to work on iOS 14.6. With all other conditions the same, running our app on iPhone 7 iOS 13.x we were able to read and write to STElectronics ios15693 tags. After upgrading to 14.2/3 the native scan prompt dialog was missing but we believe that is a known bug. Therefore we upgraded to 14.6 and now our app can still read these tags but not write. Trying to debug the issue using the WWDC 2020 nfc core demo app (linked above), results in the delegate not being called, as described by latorreSTM. Curiously, a 3rd party app, NFC Tools, is the only app we've found able to write to the tag. Therefore, writing is definitely possible, we just don't know where to look to make the necessary changes to get the delegate to fire. This is a blocking bug days before a deliverable for our client so any solution very much appreciated.