Yes, it is the S-Line. So possibly a eureka moment here. If it was standard, it might have been disabled, presumably for security reasons.
i have been looking into whether the advanced key goes to sleep (stops transmitting) when stationary, like a few others such as newer BMW keys. It’s aimed at stopping relay theft with those boxes the crooks use. If the Audi key doesn’t do this the previous owner might have disabled keyless entry to combat relay theft, in which case, re-enabling it might not be a good idea.
I did find an article on Google that says about leaving the smart bit of the key in the car and using the physical key blade in the driver’s door to disable keyless entry. Nothing about re-enabling it though unless it’s just a repeat of the same process. Might give it a try later on.