I experienced something similar last year (car was 4 years old at the time) so asked VW to investigate whilst in for service & MOT.
When A/C is switched on it made a whining sound.
It turned out to be compressor unit (or something similar) which, and to my surprise, they replaced for free leading me to question whether this is a known issue....
No harm in checking this possibility with your local stealer...?
Red