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I just had this scenario on my A4 Quattro. Roofing screw right on the shoulder. I didn't change all 4 tyres but I did change the 2 rears to keep the new fresh tyres on the same axle. The variance between the front and rear would be minimal and the AWD system can cope with that. As long as the tyres are all same brand and type it'll be fine just to do two.
I was more annoyed that I had to stick to pirelli p-zeros. Wanted to switch to michelin PS4 s but the shop only had the pirellis and we setting off for a 2000 Kay road trip.
Is there damage to the side wall?
If not I can't see why you can't repair it with a standard tyre repair kit.
If it were a sharp jagged object or a cut/tear in the side wall, then I'd be cautious. But a normal nail that's made a normal clean nail sized hole? Just plug it with a kit like this CAR VAN TYRE TIRE PUNCTURE REPAIR KIT WITH 15 STRIPS BESTSELLER https://www.amazon.co.uk/dp/B00ISFJVSG/ref=cm_sw_r_cp_apa_i_5GR3DbN0C51Q6