Stop listening to people who have no idea what they're talking about, have an agenda, or are otherwise compromised in their rational position.
If you do that, this entire idea that all is lost will become much more tempered - we have a major challenge ahead of us. Which can be said of any age (ask your older relatives what the age of nuclear weapons felt like).
In short, I deal with the hopelessness by being reasonable, and it thereby vanishes.
It's absolutely no more difficult than colonizing Mars along a similar timeline.
Everything that we face here, in the most extreme possible interpretations, can be survived by humanity with effort and ingenuity, and we even get to build our hardened shelters etc. on nice sunny days with oxygen to breathe and water to drink. Mars is MUCH harder and may also be possible.
If we're really, really ambitious and lucky we may also be able to sustain the global population we've currently got: that's a nice broad gene pool that can absorb a lot of evolutionary shocks, I think. I doubt we can expand global population much, but that won't be happening: weather alone is going to wipe a hell of a lot of people out.
It's going to start to feel a bit like bracing ourselves to live on Mars (except for on our home planet), as climate events ramp up, but humanity is definitely going to get through it. There will probably end up being a backlash against those who got us into this, as well as a predictable backlash against climate refugees that will cause a huge amount of basically genocide. It will be like 'stay where you are!' under conditions not conducive to human life. Even then technology might be able to shelter people to some extent.
"Humanity is going to get through it" doesn't feel like good enough.
Basically it's close to saying your children or grandchildren are going through some Ethiopia-style hunger and Syria-level conflict. But some will survive!
Imagine if we know before 2100 there's a chance of a devastating war all over the planet, we'd try everything we can to prevent it. Of course in reality the richer countries will probably survive (although their morals would probably be gone), although food shortages can also topple countries, doesn't matter how rich they are. Hah, I guess military might is a clever thing to have. Hungry population? The US president has decided to deploy troops to take over the grain harvest of (insert some weaker country here)...
No, it's not good enough. I see I got some downvotes: suits me, not like I actually LIKE this position. I'm just being a bit pedantic, saying that we will not be looking at human extinction no matter what. It's setting a boundary on the doomsaying, and also setting a bar for what we're gonna have to do.
I think everybody in control of things understands we will be seeing just what you say: hunger, conflict, massive waves of refugees, war. Water shortages may be even more significant than food shortages, and given modern supply chain capabilities, wet-bulb temperature conditions might be the most significant of all.
Humanity will get through this. The important question is how: and every downvoter to that comment knows that there are unacceptable answers to this. I think getting through without descending into monstrous behavior and inhumanity IS POSSIBLE and easier than colonizing Mars. But it's gonna be nearly as difficult to make happen, as colonizing Mars.
The easy out is the bad answers. That's not going to be acceptable. We're all stuck on this rock together.
If you do that, this entire idea that all is lost will become much more tempered - we have a major challenge ahead of us. Which can be said of any age (ask your older relatives what the age of nuclear weapons felt like).
In short, I deal with the hopelessness by being reasonable, and it thereby vanishes.