The one and only repair that our 08 rabbit needed over our 80k+ ownership was a valve in the compressor.
If your car is like ours, the ac compressor doesn’t have a clutch. Instead, it has a valve in it that somehow varies the geometry, throughput, compression ratio or some associated parameter.
Ours started to not work so well, seemingly being the same situation - just not blowing very cold, and then taking a long time to cool the car.
An evacuation, replacement, and recharge by mass solved it.
IIRC, it was a $100-150 job. If the vehicle is under warranty; I agree, get the dealer to work on it.