I really feel for your dd op
. It's hard to be a teenager nowadays.
My dd went through this when she was 14 yrs, two years ago. It' s hard to reassure her because climate change is a serious issue and being expats, Brexit is affecting us hugely, but I think as parents we also have to try and reassure as best we possibly can.
What we did was draw up a list of small measures we could do as a family to improve matters in a very minor way: give up one use plastic, plant trees, cut down on food waste, recycle, walk instead of drive on short journeys, instigated a second veggie food day per week etc, etc etc. We also encouraged time away from phones and were a bit more proactive about providing a place for dd's friends to gather so she was having more face-to-face interaction with them. And we encouraged sports and outdoor activities such as: horse-riding, walking, running, dancing etc as well as good sleep, healthy eating etc. I also posted technical advances that support sustainability on her SM.
I think what a pp said is true though that adolescence is a worrying and troubling time in itself anyway: you begin to learn more about the grim realities of the world, and you realise your parents are just frail humans and not miracle workers and you are assailed by doubts about yourself and by hormones etc etc, and its helpful to regularly point out past worries that didn't come to fruition, and to constantly say things like "I was worried about x but went ahead anyway and y happened which was great" or impress upon them that it's ok to be scared it's how they react to that fear that is important and although life is unpredictable, it can be pleasurable too.
The other thing that helps I think as parents is modelling how to enjoy your life and keep calm and rational. I don't always succeed at this as I am quite anxious myself but I keep having small attempts here and there and try and do the odd thing that is out of my comfort zone (eg I did scary language exam this year , went through major operation reasonably calmly apart from a few initial minor wobbles , volunteered for something I find difficult).
Dd does seem to have become a bit less anxious as she has matured a bit but there is an epidemic of anxiety out there in rl so it's not at all easy.
Good luck op 