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It's a difficult question to answer precisely, because of:
- Scientific uncertainty in exactly what the climate effects will be. It will be "bad" regardless, but exactly how bad and exactly what will go wrong is not 100% clear
- Uncertainty over how much warming will happen over the next few decades - this is highly dependent on how much action is taken to reduce emissions
- Interactions between multiple highly complex systems, including climate, the biosphere, and human societies
- The difficulty in imagining what life will be like when there are significant changes in parts of the world. One of the things people really struggled with in the early days of COVID was: "what the hell is this going to be like?!". No one really had anything to compare it to. It is similar with climate change, but on a much larger scale.
- Timescales. Even if we limit it to this century, that's another ~77 years (but the effects will probably go on for multiple centuries). It's really difficult to predict the future with a high degree of confidence.
So limiting it to the end of this century, there's a few things we can say. This is taking a somewhat pessimistic view, i.e. there won't be a substantial change in emissions trajectories over the next couple of decades.
- Climate change itself is highly unlikely to wipe out humans on this time scale. We are a highly adaptable species, spread across the planet and the temperature / climate changes won't be enough to kill us all.
- That said, there will be human suffering on a scale that is difficult to imagine. Millions will die in heat waves, droughts, floods, fires and other extreme weather events. Some regions, including heavily populated ones will become uninhabitable.
- There will also be suffering due to food and water shortages, and the spread of diseases
- Social instability (including war) will increase, due to competition over resources, migration on an unprecedented scale, and general fear/uncertainty among the population. It's possible that instability could become bad enough to wipe out humans (and possible all life) through nuclear war.
- Parts of advanced society could begin to break down, e.g. we may no longer be able to maintain reliable electricity grids
- Other species will be hugely impacted too. The rate of extinctions will accelerate, although some species will probably benefit (not necessarily species that humans get on well with).
It is pretty hard to overstate the scale of what will happen this century. It may take a while before we see the worst of it, but we're already seeing the effects, and I think within 20-30 years it will be hard to deny that climate change is affecting everything. At that point, there probably will be substantial action to reduce emissions.
As bad as all this sounds, it's important to remember that it is the "pessimistic" view in terms of our emissions trajectories. i.e. it is not written in stone. There is still time to bring emissions down to avoid the worst of it. There is also no point where it's "too late" for action. Every 0.1 of a degree that we can limit warming will reduce the impacts. So it's important to avoid "doomerism", which often just ends up being an excuse for inaction.
Even if we do restrict warming to 1.5-2C, the world will look very different to what it does today. To get to that point, there will have to be fundamental changes to global society and the economy, which will make the world unrecognisable from today. There are no moderate solutions left, it's either the nightmare described above, or a complete transformation of society. So in that sense, the apocalypse (going by the dictionary definition) is guaranteed.
