Apple Pay payments have been sitting in "Authorised" status in both test and production environments. It seems we need an API capture call to settle them, as with credit cards. (Initially, we thought this was not the case, as explained here.)
I'm not sure if we should try to capture all Apple Pay transactions. (Just learned we do need to capture them all.) I did hack my local setup to capture one, and it did indeed cause it to go to "SentForSettle" status.