Double check that the fans are doing the same thing under other circumstances first. Drive until the car is warmed up fully then let it idel. The fans should cycle to cool the coolant. If they do the same thing you're on the right track. Although, without looking up the wiring and logic I'm not 100%...

These cars will swing between 85-105 C coolant temperature at the sensor in normal operation

Running on the road, it should be at the thermostat temp or 87-90C. Stopped in traffic it will go up to 105C , the fans will come on , and cool back to 87C

Your diagnosis sounds logical. However one thing stops me from saying “fan controller for sure”. You’re only getting 0.03 vdc at the purple wire. That sounds quite low (3/100). I don’t know what the expected voltage should be. Is there any chance you misread and it’s actually 0.3? One of two things ...