The brief
The A3's handling had gone off, less stable over bumps and through turns, with uneven wear showing on the rear tyres. Those are the signs of worn rear shock absorbers. A shock absorber controls how the spring moves so the body settles after a bump instead of bouncing, working by pushing oil through small valves inside it. When the seals wear and the valving tires, it loses that control, so the rear floats and feels loose, the handling and stability suffer, and the tyres wear unevenly because the wheels aren't being kept planted. Worn shocks only get worse, and they take the ride comfort and the safety down with them, so they need changing.
The diagnosis
On the lift the rear shocks were checked, and bouncing each rear corner by hand confirmed both had lost their rebound damping past spec, one no better than the other. When both are tired together you do them as a pair, shocks work as a pair across an axle and a mismatch leaves the rear behaving unevenly, so it was both.
The work
Both rear shock absorbers came off, and a matched pair of genuine Audi-spec replacements went on, the upper and lower mounts torqued to the manual figures. A road test confirmed the instability was gone, the ride had settled, and the rear stayed planted through turns.
The outcome
A settled, composed ride, the rear planted through turns, and the handling back, with the rear tyres set to wear evenly again. The A3 went home with the rear suspension back to spec. Shocks wear together and they take the car's composure down with them, so a fresh matched pair brought the rear back to how it should ride.