With a like for like swap, the battery coding for stop/start will be the same, so no worries. The fact your dash hasn’t lit up like a Christmas tree should also reassure you.
Also, I have changed a Golf TSi battery, not like for like. Whilst initially there were lots of warning lights, after a 3 mile drive they all cancelled themselves. I still took it down to our VW dealer, and the workshop manager told me that the ECU self-learns code settings, so all was good.
Ok, my California is almost 6 yrs old and just shy of 100,000 miles. A daily driver. Twice over the past 2 weeks, after not being used for 24+ hrs, it was very sluggish turning over but did start. Charging the engine battery was fine, no warning lights when driving, alternator output to both...