Any decent battery supplier will Identify your battery from its labels, but it most certainly is an AGM battery if you've got stop start. There are battery settings in the cars control units, some cars have battery management controllers so can optimise charge cycles. I'd expect it in an AGM equipped stop start car. If there's small plugged in wire on the main + battery terminal, that's an indicator of a battery management module. If you replace the battery with the same capacity and type (AGM), then the coding will be substantially correct, but if you want you can find someone with an OBDELEVEN coder or VCDS and they can set the parameters in Adaptations in control unit 19, Gateway. I've only heard of issues talking to my motor factor, when people replaced AGM with cheaper lower capacity standard, and the AGM charging pattern was too much for the ordinary battery, and done it in in 6 months.
I'll put my OBDELEVEN on mine and grab the screen related to this later.
Btw, TFSi do use a lot of oil, my previous A6 was 2l TFSi, fabulous drive, especially with CVT transmission. I just kept it topped up. It never smoked or affected emissions test at the test centre. It appears to be a very common trait on these engines. Your oil is always fresh too, as it used about an oil changes worth between service intervals, oil would come out really clean when changing. Now that I think if it, I used to get those intermittent faults in that car, warning light, even a drop in response, which went away when on restart, and when I eventually put in a new battery.