It seems that this is a big issue for so many people at the moment. I believe that depending on where individuals are at, everyone will have to find a strategy that works best for them, I don’t think there is a single approach.
What has worked for me is to assume/accept the worst - we will all die (this is normal), all life on the planet will die (this too is normal), the planet itself will be destroyed (even this is normal) This is a fact, we all know this is what will happen, it is just a question of exactly when. Every person knows that there is birth and death. Ultimately the when and how is not that important.
Simultaneously, I use the constant awareness of impermanence and the ending of things to supercharge my own efforts to be as kind and as skillful as possible. I know I can’t control what others do, or what other groups, governments or countries do, let alone what the natural world does, but I can make personal choices. So I make personal choices of minimising harm in all ways, including living as lightly as possible, and in a climate friendly way This way I have absolutely no remorse about conduct, nor guilt about not doing what I can. What others do is outside of my control, and to take on responsibility for their actions or to feel that I have failed in trying to convince them to behave in other ways is guaranteed to result in suffering.
Ajahn Brahm gives a definition of suffering in the following terms - Expecting from Life what it cannot give is suffering. Relinquishing this, as well as the desire that humans will be other than what they are (deluded and defiled and unwise to differing degrees and in many ways) leads to acceptance and ease. Life is not perfect- life is suffering, this is the First Noble Truth. Wanting the First Noble Truth to be incorrect = suffering…
This doesn’t mean that one can’t differentiate Wisdom from foolishness, but rather that one doesn’t crave or expect that Wise choices will always be made in the world. One doesn’t despair when foolish and harmful choices are made. It isn’t good and it isn’t bad - it is just the way that it is. Even remembering ‘Good, bad, who knows’ is worthwhile. There have been many times when I myself have witnessed something that I thought would be detrimental, turn out to be ‘good’. This is the case even with extinctions… Ultimately it isn’t really about good or bad - but simply ‘different’. There is the arising of new in the place of the old. Dinosaurs > Mammals… Who knows what the future holds, it is unimaginable
The constant thing though is that we can be wise and kind in our own lives, ensure we are as harmless as possible and to demonstrate and encourage this. That is all one can do. It is only when we are expecting and craving everyone to agree and behave in specific ways that we get into trouble.
It’s ok - everything is going to die anyway. We have all died so many times before So the focus is on as much kindness as possible, to reduce suffering when and where possible, and to live in a way that generates no regrets or remorse for ones own conduct by body, speech or mind, all the time knowing that death is imminent. It helps to focus on what is really important. Living in this way - in the very shadow of death - life can be absolutely joyful and full of contentment
This helps me keep climate anxiety at bay.