Humans may survive for a long time. Societies will crumble, that's the norm, and it will happen fast now.
I think that our current civilization (western hegemony) will start to crumble by around 2030 when the western countries can't keep up their wealth and their cohesion and cooperation due to effects of climate catastrophe, depleted resources, destroyed biospheres and (in my eyes more impacting that the other factors) dwindling demographics - in concrete terms: Police, fire fighters, ambulances will not show up any longer for parts of the cities and counties due to understaffing, and that will escalate social distortions.
After that dictators will become the norm (they are on the rise already), and due to the notoriously incapable and destructive tendencies of such regimes wars will eat up the rest of the humanity and the collaboration we need to function on higher levels (states, continents, worldwide). My estimation is that this point will be reached by around 2100.
After that the game is open. My guess is that humankind in the long run will return to some kind of self sustaining agraric communities with skilled guilds likewise late middle ages plus some added comfort and medicine (a lot of our current knowledge is completely useless without a global network for resources but stuff like hygiene, electricity, mechanics etc. on a small scale may survive).
Wild guesses, I know. Please keep in mind that I stated "will start to crumble by around 2030" - that date is a very soft point which will not come with one single big bang but with a lot of "small" incidents.