Actually, the world is not doomed and neither are you. Human kind has already experienced two horrifying world wars – and survived. Besides, throughout history, since the existence of humans, there are always wars going on somewhere in the world at any given time. In every case, there is always a post war. It always seems like the end of the world to anyone involved, but the Earth always survives. Times get bad, but eventually times get better and sometimes even gets really good. Note that Hiroshima and Nagasaki were both bombed with atomic bombs. Today, the radiation is gone and both are large, thriving cities. There are even living survivors today.
The climate crisis will get bad – really bad, but it will not be the end of the world. When it is said that global warming is destroying the world; it is the plant an animal world that is being altered to an extremely inconvenient state, but the Earth lives on. Actually, the world has been there before. However catastrophic, it is not going to end during your lifetime. How bad it gets will be dependent on everyone’s actions – including yours. Regardless how bad it gets, it's very unlikely you will be killed by it. Though you probably can’t see this in the moment, but society needs you.
It is still possible – actually very likely – to have a productive, fulfilling, happy life. Suicide, however is failure by default. Failure for not even trying is a shameful failure. Suicide ignores the likelyhood that no radiation poisoning or any other agonizing death will occur. I suspect the reason you “can’t just do it” is because deep down, you actually know that.
Obsessions are like addictions. It's a positive feedback loop. You get fixated on something and it becomes an obsession, but that doesn’t mean it is real or productive or healthy.
Hang in there and find a more constructive obsession. Believe it or not – we all need you.