Maybe this helps a little more to solve the problem. If I open the shower plus the vanitori the Calefon turns on but if I close the vanitori and leave the shower open the Calefon turns off.
The shower is higher, that shortens the distance with the base of the tank and therefore has less pressure. opening the vanitori that is lower increases the pressure and partly the flow rate.
The reasons and solutions are what happened before. If finally the pressure is not enough for this new water heater, you will need a pressurizing pump.
Most likely, you still have air in the pipes. If you stick your ear to the water heater and hear noises, those are the air bubbles.
Send water in the opposite direction to push them into the tank, hitting the water heater with the palm of your hand.