A closed loop is probably easier to maintain compared to pumping caustic saltwater and all the things in it near batteries.

You really don't want to cool anything with sea water directly. It's corrosive due to the salt and contains all kinds of fun things from flotsam to critters, some of which might make a home in your cooling loop. in this case, additionally, sea water is conductive and that's not acceptable in a battery.

However, feeding the coolant through some sort of heat exchange with the sea water is very likely something they do.

[delayed]

Yes, that's the absolute norm (you often also want to cool the exhaust pipe itself and there you often see coolant water pumped straight into the exhaust). That's the obvious thing to do: You do have a huge reservoir of readily available coolant, tapping it is the sensible thing to do :) That's why I fully expect them to run their coolant through some heat exchange with sea water.

Fossil fuel engines are significantly less efficient than electric ones... so need a lot more cooling. I'm sure getting rid of the need for that would be a nice win that might be practical with electric engines.

Batteries and electric motors are fussy about temperature, you still need thermal management. Probably not as large a system, but you might need a heater or sub ambient capability.

Yes they are.

Also saltwater is conductive so if you submerged your batteries in it, you'd have an immediate short circuit. It's definitely through a heat exchanger.

The immersion fluid has to be non conductive and non corrosive. Hence the choice of oil (flammable) or weird fluorocarbons.