For clarification: there are 3 different charging states for the P2 & P3 phones: "slowly charging", "charging", and "charging rapidly".
USB PD is capable of "charging rapidly". USB A to USB C is capable of "charging"; depending on the USB A connection. An old legacy device USB A that only puts out 500ma will show "charging slowly"; a modern USB A connection (such as a head unit) will put out 1.5 amps and will show as "charging".
The core issue is this: in the exact same environment (cables, vehicles, head units) when connected to an AA capable infotainment system, the P3 shows "charging slowly" whereas the P2 shows "charging".
In my experience, the P3 does not even come close to charging as fast as the P2 in the exact same environment. In fact, it would charge 1/3 as slow as the P2.