Did the detailer who applied the ceramic coating not give you any advice - or a leaflet from the manufacturer of the ceramic coating - on washing and aftercare? You’ll no doubt have invested quite a lot of money in getting your car ceramic coated, so IMO appropriate aftercare is important to maximise longevity and durability of the product.
As @ramrod has said, avoid the hand wash places. They tend to use quite harsh products so they can speed up the car washing process to maximise the number of cars they can ‘clean’ (time is money them, so more cars = more income). These harsh cleaning products can strip conventional wax and sealant protection off the car - not sure if they reduce the longevity or durability of a ceramic coating though, but I wouldn’t risk it anyway.
I’d definitely avoid letting the VW dealer do their free ‘scratch and swirl’ treatment (a.k.a. complimentary free service wash), unless you want their sponge monkey to rub a grit laden sponge over your car and use the same bucket of dirty water that’s also grit laden and has been used to ‘wash’ numerous dirty cars before yours. I always specifically instruct the dealer not to wash my car, and put my ‘do not wash’ hanger on the interior rear view mirror, tie a ‘do not wash’ tag on my keys and get the service advisor to write the same instruction on their job sheet.
I’d definitely recommend continuing with the two bucket wash with a lambs wool mitt (I actually use three buckets; the third one has a separate shampoo / water mix for the wheels). I’d also ditch the Tesco shampoo and use a ph neutral shampoo. Consider doing a pre-wash (snowfoam and rinse) stage to loosen and remove any dirt before making any contact with the paintwork. I minimise contact with the paintwork when drying - I have a warm air dryer (Metro Vac Sidekick Blaster) to blow the water off the car, and then mop up any residual water drops with plush micro fibre drying towels (pat dry, rather than rubbing or dragging the towel over the paintwork).
There’s a useful article at the link below on best type of shampoo for washing a car with a ceramic coating, and tips on washing the car;
https://avalonking.com/blog/what-are-the-best-automotive-shampoos-for-ceramic-coated-cars/