Who will be closest regarding what life James Webb finds.

[Anomalocaris]

The circumstances of their extinctions are not to be found with humans.   Humans, by crafting tools and  planning in a versatile manner, and by eating each other metaphorically speaking, have achieved the adaptability to eek out continued existence in virtually every environment where any land quadrupeds has adapted to survive.    Therefore remnant but viable human populations can be expected to survive any event or process through which some percentage of land mammals, reptiles or birds survive.     So I think human specie would likely likely survive any of the great global extinction events known to have afflicted the earth in the last 600 million years, including sudden onset events such as K-pg impact that did in the dinosaurs, or protracted events such as end-Permian extinction.  

We may not be quite as hard to eradicate as cockroaches, but we are probably close.

I think the only real chance for humans to extinctify ourselves will come from humans collectively embark on some truly monumental geo-emgineering projects that becomes self-sustaining amd then go awry,  and result either in true run-away green house effect or a repeat of snowball earth that basically does away with all large land dwelling animals. 

And we are not that cooperative or have our acts together nearly enough to do that.