I think this is to do with countries and I’ve seen it happen when making redemption bookings with a foreign-to-me city of departure.
You were booking ex-LUX and presumably your BA home country is not there.
Usually if you scroll down to the credit card details, the system will probably have auto-selected that you have a Luxembourg credit card. So it doesn’t offer your saved cards.
Had you changed this card country to your home country, it’s likely your saved card would have been shown.