I think I’ve fixed it!
I noticed that the option to deactivate the digital key in the MMI settings was greyed out (I guess because there was no digital key setup). So I re-added the digital key to my phone and was then able to deactivate it in the MMI.
So now, whilst I now have the digital key in my iPhone’s wallet, it doesn’t work by me just walking up to the car and opening the door. And also, once in the car, I am no longer getting the message to set up a digital key.