It sounds like they fitted a correct aftermarket equivalent battery ie an EFB one.
You can't check anything to see if they recoded the car to recognise that it has a new battery, all you could do, if you had a proper VW Group compliant diagnostic tool, would be to check the battery stats to see if they looked like the battery was replaced with a new one recently.
I think, that with time, the car's battery charge management system will adapt itself to be optimised to that new battery's improved health, so maybe wait a few weeks and see if things improve.
I would hope that any car garage that replaces car starter batteries in Stop/Start car knows that the new battery needs coded into that car.
There is just one other issue, if the BMS dongle that is on the battery -VE post is not doing what it should, then maybe that is what killed the previous battery and will go on to force the new battery to an early demise.
I plan to replace the EFB battery in my wife's August 2015 VW Polo with an AGM "sometime" ie after it hands out its first "I'm not too well" message, I have bought a new BMS dongle to fit at the same time, unfortunately these BMS dongles cost quite a bit, but there again so does replacing the car's battery every year!
I bought a cheap plug in 12V DC digital meter, and it lives in the front power socket, so that I can keep up to date with battery charging.