Why Current Will Not Pass in Induction Furnace Water

Water will pass through the center of the coils.

The current will pass through the skin of the conductors (skin efefct, high frequency source)

Permeability of water will not assist in overcoming the skin effect (almost equal to air, and of course aluminium or Copper and 3rd to 4th degree less than steel).

So the water filled coil will almost electromagnetically act like solid conductor and as we know, there is no current through the center of the AC and more so in high frequency power conductors.

In the back zone (pumping) - the insulations (as the above post mentioned) and the earthing will be enough to save the pumps from the micro current that still dares to go there.