The user damaged their battery by plugging in a 2KW inverter. Then they complained that tesla would not give them a free battery as a result. So it seems somewhat clear that Tesla denied replacing the battery in this situation

They said "the warranty is void". The pivotal issue is, is it the entire warranty? Or just some sort of sub-warranty on just that component.

We don't know what they said. We are getting second hand knowledge. We know they wouldn't replace battery.

The standard approach here is warranty doesn't cover the part you damaged through misuse. So if you stab the car seats with a big knife, they won't give you new seats, but that doesn't void whole warranty.

Some things do void entire car warranty, those are pretty standard as well. Things like salvage title, submerged in a flood etc.

Others void out powertrain warranty or larger areas, usually pretty logical (flash cars computer with a tune, race car and destroy engine probably one of the more common ones?) Even though just engine may be obviously destroyed, you might lose warranty for entire powertrain (clutch / transmission etc).