At what point do the phytoplankton I'm currently breathing the poop of have a mass extinction event? All of human civilization is about to drown on dry land and I spend 5 days a week maintaining software that charges people for turning on their lights.

You're worrying about the wrong thing.

You're far more likely to die from nukes. Humanity is not going to be made extinct by the direct effects of climate change. What's far more likely to happen is climate change leads to societal instability which leads to the nukes flying. By the time phytoplankton reaches the point of mass extinction, humans would have long since wiped out every single vertebrate and most invertebrate with nukes.

And by wiping out vertebrate life with nukes, you don't have to nuke every single square inch of earth. You just have to nuke enough cities to cause gigantic firestorms which blanket the Earth with smoke ie nuclear winter. There's a debate among scientists on how much cities you have to nuke before the snowball effect happens, but with enough nukes, it'll happen. Nuclear winter and societal collapse means the population starves to death. If you aren't the lucky ones to be instantly vaporized or turned to red mist by pressure waves, you'll either die from radiation poisoning or starvation. It's starvation that will ultimately kill humanity if the nukes start flying.

As a final note, you should read about all the close calls we had towards the "nukes fly everybody dies" lose condition of humanity. So many close calls. Outside of complete and total nuclear disarmament, our luck will eventually run out if we don't do something about it.