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Well, the battery is not a single monolithic design, it is composed of thousands of small (think AA) cells. My uneducated hunch is that that design helps them extract power from many cells in parallel. It's also huge, taking almost all the floor of the car.

Not sure how they cool that beast though.

The batteries are actively liquid cooled.

There are lithium polymer batteries with a peak discharge rate (usually a few seconds) of 100+ times their capacity (C rating).

So if you put a lot of those single cells in parallel to e.g. form an 80Ah battery, you could for some time pull 8000A+ out of it at 3.7V (the car's motors probably need a few times that voltage, so there will be cells in series).

I think you're an order of magnitude low; the battery is arranged to give 100x that voltage and still put out over a thousand amps.

But we're looking at batteries with 23k amp hours across all the individual cells.

Put enough AA batteries in parallel and you could get that much current out of it.