Stephen.
All your voltage readings tell you is that the alternator is working and that there is not a short circuit in the battery. They tell you nothing about the condition of the battery in regard to sulphation of the electrodes or the formation of dendrites which cause loss of capacity and an inability to hold a charge. To do that requires equipment that most owners do not possess so I suggest you get it professionally tested.
As to coding, I have read (though I can not recall the source of the information,) that all VAG cars from 2008 require it, and some earlier models too. (My 2007 A3 did.) Uncoded new batteries will still work for a while though their lifespans will be shortened because of wrong charging rates.
Incidently loss of radio presets and false dash warnings are symptoms of a battery that is dying. See this post:
https://www.audiownersclub.com/forums/topic/28121-ignition-light-disco/#comment-113216