I have had a look at the Itsme website and they do claim on one page that the application should work with a UK passport. That is positive news. Looking at another page, it says that for use with several Belgian government services, you will need an itsme account linked to a Belgian form of ID. There is something called a 'rijksregisternummer' which is a number only stored on Belgian forms of ID and linked to your identity. If the Belgian authorities set up the app to look for that particular number, it won't find it in a UK passport, even though the app developers state that a UK passport should work.
The additional puzzle is why you could not get your credit card to work on your phone, as that points more towards a NFC chip reader/reading function failure. But your visit to the Apple store appears to have answered that question.
Just to be sure, you could get in touch with the support department for the itsme app using the form on this site:
Submit a request – itsme Customer Support Unfortunately, they do not appear to offer any other form of contact.
I would also consider contacting the Belgian government department that you are trying to deal with. If the app has been set up to look for the Belgian registration number on your ID document, this is something they should know about (hopefully). Do they have a phone number you can ring?