You have a Sinamics S120 16kW SLM on the front of your servo system - and your largest motor load is 13A 3-phase (spindle) and your axis motors (assuming they are all the same) are 4.5A continuous . . . assuming that you are pulling continuous current from all of them simultaneously you have 13A + 4x4.5A = 31Amps (I see what looks like 4 motor leads going to the pair of double motor modules).
Looking at your line up you have a 16kW Smart Line Module (SLM) on the left - this is a bi-directional power supply that you feed with 3-phase and it develops DC power for all of the drives. The DC bus passes from left to right under the light blue covers running along the top.
Next module to the right is your spindle drive . . . a SMM (Single Motor Module)
Next module to the right after the spindle is a DMM (Double Motor Module) which could be X and Y
Next module to the right after the DMM which likely is Z + a rotary axis?
The Smart Line Module (SLM) is line regenerative, i.e. if you are stopping your spindle and all your axes simultaneously, all of the braking energy from decelerating the motors pumps up the DC bus . . . when the DC bus gets sufficiently high the drive front end is an inverter that pumps that energy back onto the line and feeds power back to the utility. Thus, this system does not require braking resistors.
Realistically, you can likely get away with 25 Amps for the drive system. I don't know what else you have for loads (coolant pump? control power transformer?).
I wouldn't attempt to run this with a VFD unless you like smoke and fireworks.
FWIW, I have run that model of 16kW Smart Line Module from 240V three phase with no difficulties - but that will limit how much power you can pull off the DC bus and your maximum speeds on your servo motors will be limited as well. Typically your system would also have a SITOP 24V power supply that may also tolerate operation at 240V, you should double check this . . . so if you can live with less than rated power, then run it at 240V. You "may" need to adjust a low voltage threshold on your controller . . . the voltage thresholds are adjustable with the Sinumerik controller. But you will need to know the password which is well known if left at the standard Siemens default but who knows if the OEM has altered it.
If it truly is a 3-Axis system + spindle you would likely be fine at 20Amps @ 480V using a 240:480 transformer. If you can find a transformer with adjustable taps, this would help with balancing the voltages which would make the regenerative front end on your drive system much happier.