I would argue it depends on the method humans get removed from the equation. Chances are, humans are going to leave behind such a mess of that it’s going to be pretty hard for most things to survive.

Anything living off hydrothermal vents should be fine, even if the Earth undergoes prolonged nuclear winter or even a snowball earth scenario. Everything else is at great risk of going extinct. Tardigrades should be fine though, since they can survive all sorts of weird extremes.