This is my googled understanding, take with a grain of salt:

Batteries contain of lots of individual cells. If you short-circuit one cell, you generate lots of energy (from the short-circuit), and start a chemical reaction (fire) that does produce its own oxygen. Once that cell has lost all its charge, the reaction would stop, but until then the fire has compromised neighboring cells, which start the process all over again.

Water won’t stop the first broken cell from discharging, but it can bring the battery down to a temperature where the fire is too cold to sustain itself. It contains the damage to the cells that are affected already and prevents more cells from igniting. This is how you stop a battery fire.

The car gets put into a tank for several days to allow the broken battery cells to discharge safely, without overheating and causing another fire.