You should be able to recode a new battery via CAN Gateway - in Adaptions you will find a list including battery capacity, manufacturer and serial number, typically only the last digit of the serial number needs changing.
Just make sure that you buy an AGM battery as it seems like naughty Audi has been sending too many cars out with just EFB batteries!
Tayna sells Bosch and Varta - and others, so it should not cost much more than £180 for the correct frame size AGM battery for your car.
A friend with an A6 2.0TDI first reg'd in December 2016 had this issue last week, his factory fitted battery was just an EFB, he replaced that with an AGM, or at least his "all marques" garage did.
My daughter has an end of April reg'd SEAT Leon Cupra and it has an EFB battery and I tested it last week and it is dying quickly.
My wife has an August 2015 VW Polo 1.2TSI 110PS and it has an EFB battery and when I tested it, it has suddenly dropped off very badly - no indications that it is faulty yet, but now that I know that it is well past its best, I should really buy a new AGM battery and avoid any inconvenience.
This was thought/said to only be a Moll brand EFB battery issue, but maybe there are more duff batteries being supplied than we think, not good when it happens to you!
Edit:- it is only right to add in here that my 2011 Audi S4 with its factory fitted AGM battery, still seems to be okay, it does not get used much and while not being used is always connected to a CTEK charger/maintainer/tester - so I'd think that that helps a lot to extend its useful life. Its original battery is a Varta brand though listed on the BEM label as JCB - which normally means a Johnsons Control made battery.