Identify specs of this filter coil and enable independent use of PSUs fed through it?
As the modules say they are standard power supply modules that can be directly fed with 230VAC mains. The choke might just be to limit inrush current as there are multiple power supplies in parallel. If you are worried about mains filtering then put a mains input filter module there. if you experience bad noise on DC output, it won't be removed by input filter as these are switching mode power supplies.

The inductance and resistance of the original filter coil can be measured with LCR meter, but there is no way to figure out the surge and operating current rating. Only hope to know them is by finding the AC input surge and operating currents of the power supply modules and add them up. But the power supply modules already seem to have proper mains filtering and NTC surge limiting so unless you intend to power all of them with a single mains switch or plug you don't need extra surge filtering.