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.
It's already making things hard. Unless you live in a cave (and even if you do, quite probably, IDK) you'll have noticed an increase in the frequency of what's euphemistically called "extreme weather events". These things are bad for us, but even worse for crops, and they're going to keep on getting worse.
The world has lost /is losing a lot of food this past year alone. Saw an article that Georgia (US) lost 90% of it's peaches this season, folks/farms from the Midwest and Canada either couldn't plant at all due to lack of rain or what was planted has died already.
The dam that was blown up in Ukraine ruined a huge area of farming that has global significance as they exported a lot of grains and oil seeds.
Spain is facing over 60% crop failures and the third year without honey.
Cotton crops from Texas and Spain also at a huge loss.
I am sure there's more, this is just off the top of my head. It'll take a little bit for it all to show up, but we are definitely going to be feeling the effects of this by next year I'm sure.
“The apocalypse is not something which is coming. The apocalypse has arrived in major portions of the planet and it’s only because we live within a bubble of incredible privilege and social insulation that we still have the luxury of anticipating the apocalypse.” by Terence McKenna
End of most life. We are already in the sixth mass extinction event, the Holocene extinction, which is characterized by an extinction rate that is 100 to 1000 times higher than the normal background extinction rate and is also 10 to 100 times higher than the extinction rate of any prior major extinction event in the history of this planet. (Source) It is, however, unlikely that all life will cease to exist since there will always remain habitable zones on the planet. A true runaway greenhouse effect like the one that likely happened to Venus is (very very probably) not possible, because there is literally not enough CO2 on this planet to push Earth into complete inhabitability (Source) It will happen to the Earth naturally in about a billion years though since the sun will have become ten percent brighter by then, which will first turn the oceans into water vapor (accelerating warming via runaway greenhouse effect) and finally turn the entire planet into one big desert with surface temperatures of over 900 degrees Celsius.
Depends on what you mean by apocalypse. That term didn't originally mean the end of the world, just an event so massive that the world was forever changed by it. It won't be the end of humanity, but we're running out of time to prevent it from being the death of billions. Pick your definition.
I think it very unlikely that it will end life on Earth. There are organisms that live in volcanic vents in deep ocean water. Something will evolve to fill whatever niches are available as the environment changes.
I also think that humanity will survive, but even that is not certain. How many individuals die is going to depend a lot on how well we deal with the underlying problems and what technology we are able to develop for surviving under the new conditions.
Hard life.
Followed by Shit life.
Then Extreme shit/hard life.
Then Apocalyptic life where resources are scarce because of extreme climate.
Followed by extinction?
I mean eventually it's coming.
That is going to happen regardless. The things that are causing climate change are the same things that make life harder and more expensive (governments and corporations striving for maximum profit).
It's not an existential threat to humanity nor is it even a bad thing for everyone. It highly depends where you live. For many countries the climate refugees are probably going to be a bigger problem than climate change itself. It's a net-negative for the earth as a whole though I believe.
I'm worried that we won't be able to support the population we have. Lower quality of life I can handle. Famine and starvation is frightening. I hate to say it, but we'll probably be ok in North America. The rest of the world, fuck.
We're projected to reach temperatures not seen in more than an estimated 20 million years due to our actions within a couple centuries. Harder may end up being a massive understatement.