We only know of one rock in all existence that's habitable to humans or literally anything else. Relative to humans, yeah life finds a way cuz it's a lot more resilient than us; relative to the kinds of extremes the universe of capable of producing, life is SUPER fragile.
So... yes, humans are fucked, but so are a lot of other critters, and who knows where all the feedback loops we've unleashed will end after we're gone. Shit isn't going to just magically get better once we're gone.
Hopefully it'll stabilize, but there comes a point that even the most hardy of extremophiles can't survive, and if we cross that line, Earth becomes indistinguishable from every other lifeless rock in space.
I mean, hopefully. They are people that have driven drunk many times and been fine, but it only takes one incident to bring that trend to an immediate halt.
We have no way to tell if conditions will stabilize within the surviveability window of any specific critter. Nor can we claim all life will for sure be fucked - point is we don't know.