This is one of the reasons I'm quite pleased to have a Mercedes now rather than an Audi. The petty pointless recoding to fit a battery was one of the many annoyances I found with Audi. It's a battery. The onboard computer should be able to work out that is changed without needing to be coded.
On the trickle charger front, I can sort of recommend the ctek chargers. I've had one for a few years and it does a super job of reconditioning and charging. The only irritation I have is that the button that changes the mode seems to stop working after five years - all too common. I think it must corrode. Fortunately pressing it like a million times seems to eventually work. Other than that robust and very good. I'd definitely try one before a new battery.