The US class settlement never actually found VW responsible, nor did it confirm they were not responsible. Thus it left everyone in a bit of a no mans land. VW denied there was an issue, but they did agree to extend warranties 12 months to allow owners to potentially claim a repair under warranty. That ended in 2022. So it’s unlikely it would have been any help to you even if it applied here.
The specific engines concerned were designated EA888. If there’s a recall or service programme applicable you can check via VW. I suspect unlikely given that they’ve never accepted liability for any problem.
There’s a garage in Huntingdon UK called The Car Edition, who do excellent YouTube videos showing their repairs. Many all of which are German cars with common and expensive problems. BMW and Merc timing chains, Audi & VW gearboxes, BMW manifolds, all sorts. And on all sorts of cars, when they do a cambelt change, they see leaking water pumps - so it makes sense to change them. You say it has only 53000km, but how old is it? VW relatively recently massively lengthened the intervals for changing the belt - if yours was originally on the old, shorter schedule that could well be a factor. In any case, if your car is (say) 8 years old, well a leaky water pump isn’t that unusual.
If your garage is saying 1000€ for a water pump change, to do it they have to remove the cambelt and accessory belt. Nobody in their right mind would re-fit the old ones, so in fact that’s not too bad a price if it really does include all that work, if it’s genuine VW parts at a VW concessionaire. Norauto would quote you around 600€ for the job including the accessory belt - but not VW parts. They indicate 6 hours - given that a main dealer rate is around 100€/hour - well it adds up!
Anyway, reminds me of the old advert: If only everything in life was as reliable as a Volkswagen!! Don’t you just love a good old mythological story?