Indeed, I checked other types of service on the booking system as well (which indicated that there was availability for those other services), so it seems that they are not allowing booking appointments for annual marriage extensions at the moment. Perhaps it's another ploy to shift more people onto the less laborious retirement extensions instead or to use agents.
I was wondering whether I could physically visit CW in person to make an advanced booking appointment a month in advance, or whether it can only be done using the online system?