Contactor Coil Voltage – What is the Coil Voltage of This Contactor?

You don't want to suppress the inrush, but rather, find a different way to supply the inrush current — it is required for the contactor to operate properly. It needs about 30 A for up to 50 ms, or about 1.5 C.

If you are willing to allow your supply to sag by, say, 6 V, then you need about 1.5C/6V = 250mF of capacitance to supply the short-term current.

You can use a low-value resistor, thermistor, or inductor between the power supply and the capacitor in order to isolate the power supply from the surge.

It looks like the coil needs a maximum inrush of 32VA at 60 Hz, so you have some power left over to drive a controller. The holding current is much less, so if you have a big enough filter capacitor on your Arduino power supply to last through the inrush, you can use more average power.

In the future, please provide your own links to the relevant data.