I have managed to resolve the issue but the solution is very surprising. I noticed that the regular outlet charger was still plugged into the outlet and decided to disconnect it, fold it and put it back in the under-trunk. Although it was not connected to the car, the moment I disconnected the old charger from the outlet, the Tesla started working with Gen3 charger with 16A on 3 phases. Upon reading, I found that if I put it on 20A circuit (the breaker is 20A and in the Gen3 charger setup I wrote it has 20A), Tesla will actually charge the car at a maximum of 80% of the current (20A*80%=16A).