IMO, successful doesn't necessarily imply success every time - only more often than not. Failures can create learnings which lead to future success (cf Edison's experiments in the electric light bulb).'Success' is invariably followed by failure, and long success often by rapid failure.
At the risk of repeating an often used analogy: The yeast was a remarkably successful species- until the loaf went in the oven. Even then most of the yeast were still convinced that things had never been better..
As far as we know yeast doesn't have the same level of self awareness or consciousness as humans. And if it did, we don't know that it isn't screaming "I'm dying here, but blimey that was a great party. #worthit". Everything dies in the end. Having had a few close calls myself - I can report that for all of the pain and suffering involved in the process, it's manageable - even OK and quite interesting.
Even so, yeast is still thriving and successful as a species - even if individual populations are regularly wiped out to make our daily bread.
We also know that humans have made choices in the past which have avoided extinction or extreme population loss and are probably getting better at doing so. That said, there are definitely still dangers - particularly over the next century or so.
To address your other point, I've found the best way of dealing with climate anxiety is to take individual action at the domestic, community as well as lobby for national/international action. Decide what you are willing to do, do it - and then stop watching so much of the news works for me. Sure it might be a lost cause, but it might be better than wondering whether or not to stamp on a doorstep slug to protect its progeny from getting poisoned (who are we to decide on their behalf anyhow?)