Excuse my ignorance, but is water the right way to put out a lithium battery fire?
Eh.. this is why 'safety' is such a vague thing and is usually treated as lowest common denominator when technically 'it depends' on soo many things.
If there is nothing nearby which is ignitable the safest thing to do is not mess with it!
If there is something nearby which is ignitable and can be moved without exposing yourself to danger, just move it.
I think actually disturbing/messing with the fire
itself comes after that or only if that is not possible.
But 'putting out' a fire is not always necessary so much as 'keeping other things from catching on fire' is. Pouch cell is guaranteed hot garbage (ha jokes) whether you put it out or let it burn, so putting it out is optional. Keeping other things from burning is more important.
Keeping other things from burning or catching on fire could be multiple forms such as slowing conduction of heat from source to it, or lowering temp of source by conducting some of its heat away into something cooler that you don't care about heating up (putting water on it could work, dirt, flour, etc), lowering temp of thing you are trying to avoid igniting (spray it with water probably works), add thermal mass to thing you don't want to ignite (water works again, if you can spray it periodically or constantly). Even just spraying water on the ground in a circle around this fire would be a viable way to prevent damage to the concrete (charring/cracking/spalling etc).
So just because water might not be the 'right' way to 'put out' a fire doesn't mean you don't have a range of options of how to use water to keep a situation from escalating. Directly spraying it onto the thing that is on fire may not be the best way to use it, but its also not the only way to use it. I can't think of many fire situations where water would have no use at all. I think the main thing is to think before you act. You don't want to make a tiny fire MORE dangerous by indulging your knee-jerk reaction impulses. I would venture that the likely most important first thing to do in most fires is actually to protect your eyes and lungs and THEN think about managing the heat energy.