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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.
I don't know if I can repair it. Run flats. Fuck knows. I'm going wallet out, safety first and replacing.