Old and new tyres on one axis – problems?

Even in order to avoid the slightly humiliating hint “Gucke du Sufu!”, I looked around here and on the whole web. But also the local thread to Abrollradius/Mittedifferential did not really help me. What is it about? I drove into the left rear tyres (V6 TDI) a nail or something. One sees the thing on the tread silvery shine. The tire loses within 24 hours 1,9 bar. The tread depth of the tires is between 4 and 5 mm. A new tire has, as far as I know, 7 mm. This means that the wheel radius on the left and right is different if I only renew to the left. Whether this means something, and if so what, one was not quite in agreement at the time in the above-mentioned thread. Is there any further findings by now?