In short:
VW used to have Castrol as their supplier for OEM and aftermarket recommended oils.
But relatively recently they have switched to Shell as their OEM supplier.
Personal experience:
My car was purchased in 2018 (albeit with a 1.5 engine) and the engine oil cap has Castrol branding. I have used Castrol 0W20 LongLife IV for the last two years on it, and it was good. No complaints.
But for the last change I did, Castrol was not available locally. The parts distributors had VW original 0W20 LongLife IV oil, which was produced by Shell in Germany. Also no complaints there either.
The price difference for these two is negligible, at least in my country. Generally speaking, for modern synthetic oils, they are 95% identical no matter the manufacturer. They mostly differ in the detergents, resistance enhancers, and other additive packages.
In essence I went from a green hue of oil (Castrol) to a turquoise hue (Shell/VW original)
As far as to which oil weight to use... That is up to you. These engines can run both 0W20 and the classic 5W30. There really shouldn't be any
problem to use 0W30 even, as it sits in between those two, but dont quote me about 0W30.
0W20 decreases fuel consumption (EURO 6 norm), and will lubricate better during colder temperatures.
5W30 will fill in the mechanical gaps better, and has been proven for decades as the go-to weight for most engines.
Some mechanics have their skepticism about the long term effects of 0W20, once the engine has >50/60/70 000 km, as the engines mechanical tolerances will inevitably decrease over time, and it will require thicker oils to protect the engine. Hence, they suggest that we switch to 5W30 after that amount of kilometres.
Yet on the other hand, manufacturers like Toyota recommended 0W20 for the past 20 years on their cars, and I did not hear about any major problems with it.
As always there is a lot of internet disagreements about these topics. But the golden rule still applies, as long as you maintain the car regularly, you should not have any problems, no matter the oil weight and manufacturer.
Hope I helped.