I had the P7's for a while on my last car and they were very noisy too, with poor wet grip.
I found over the years that tyres can make a huge difference to in-car noise levels.
The noise ratings on tyres appear to be a good guide and even 1 or 2 dB is noticeable, but it also depends on the frequency (or pitch) of the sound, i.e. lower frequencies bother me less than higher ones.
Bridgestone claim 71 or 72 dB for the Turanza in 225/40 R18 depending on the variant. The quietest tyres for this size seem to be 70 dB.
On the plus side, these Bridgestone's do seem to be grippy in the wet.
I suspect the A3 is just not as quiet as it's supposed to be. I had a Volvo V40 and Seat Leon before I don't find the A3 any quieter, but not louder either roadnoise wise from tyres. Wind noise I think the A3 is pretty quiet at highway speeds, when the highway is smooth surface! Can hold a conversation with all passengers. I had Bridgestone on the Leon and Michelin Primacy 4s on the V40. However they were 205/55 R16s and the A3 is running 225/45/R17 (Pirelli P7 C2). Maybe your car just is an S line with less suspension and a thinner sidewall 40 profile. Had a courtesy A5 running 245/40 R18s, and that car was quieter both wind and road noise (well it better be it's more expensive!)
In regards to the wet grip, I have no issues, during one massive thunderstorm in August, massive rain requiring wipers to be on high and it still wasn't fast enough, going 65mph on the highway it was fine.
I have these on a 35tdi S Line from new, no issues to report seem to be good tyres although not done a winter yet. Noisey on rough tarmac but quiet on smooth roads, these were fine in terrential rain the other week so happy with them.
The other thing is they are getting close to needing replacements on the front at 15k miles not sure if they will last till spring.
What have people been getting from these mileage wise?