Battery fires are not hotter. An EV battery fire and ICE car fire actually have fairly similar heat energy profile. ICE cars are a bit more intense. There’s a study from Sweden that set fire to similar ICE and EV cars and measures the energy. A gasoline tank will typically store a lot more raw energy than an EV battery.

They are self oxidising if the electrolyte burns away. That’s true. The anode and cathode is shorted and you get thermal runaways. That’s why it’s a bit of a challenge to fully put out a battery fire. Next gen solid electrolyte batteries fixes that to some degree.

Of course you can extinguish a battery fire with a fire extinguisher, or just water. The problem is that thermal runaway will make the battery really hot again, which will reignite anything flammable around the battery. So you need to keep it cool for a long while, generally by spraying or submerging it in water.