You're absolutely right - they're correctly anxious because the future LOOKS grim.
But the world has always been pretty grim: For most of humanity your existence was focused on sustenance. Then, once starving was taken care of, of not dying of some preventable disease. The privilege of self-actualization and even having to consider what the future of the earth could be is relatively new. We can certainly then look at the 50's and say well that was prosperity, and even ignoring the unique economic circumstances of the aftermath of the deadliest war in human history, everyone who grew up in this "prosperity" certainly wasn't very optimistic about the world. They were constantly living under the terror of global nuclear annihilation.
Except...they weren't. AHA, and here we come to the truth: To survive, and because doom gloom and anxiety were not to be tolerated, everyone bought into the propaganda. People did "duck and cover" drills and expected to survive a nuclear blast. People genuinely believed (in the West, and in the East) that eventually their side would prevail, and there'd be nothing to worry about.
People built, people invested in the future, because they HAD to. And then did the hard work of arms talks, detente, etc.
What am I trying to say? I think every generation had the right to be CORRECTLY anxious about the future being pretty grim. And this generation is the first one that is being told that it's valid to feel anxiety and to not just stifle away feelings.
And yet....I can't help but wonder if the only way humanity can get itself out of trouble is actually with some blind and empty optimism. Climate Doomerism is even infecting the left, and sites like this. "Why should I have children if the world is going to melt? Why should I reduce my carbon footprint if Exxon won't?" (btw. your carbon footprint stimulates demand for fossil fuel products that Exxon then provides. anyways)
To fix giant humanity-scale problems you must believe and have an optimistic outlook on the future of humanity. That doesn't mean sticking your head in the sand sand saying "everything will turn out fine", but it does mean saying "Yes, we CAN decarbonize. Yes we CAN create a more fair and equitable world for all. Yes we CAN maintain balance with our ecosystems and not wipe our species or every other one out."
And the teenagers need to hear it cuz buddy THEY'RE the ones who have to do it. It doesn't matter if it's hard. WHAT OTHER CHOICE DO YOU HAVE. Well, I suppose Suicide is one answer. I suppose I have heard that when depressed people kill themselves it's because the pain of existence is worse. I never understood it. I care too much about my mortality. I don't believe it. I think the increase in THOSE numbers is just based on more accurate reporting. I don't think teens are killing themselves because they're anxious about the economy or climate change.
Of course it's not the teens that should be held responsible for finding that optimism. It needs to be generated and nurtured by the adults around them, and in the media. And I don't mean consumerist influencer optimism, I mean people like Carl Sagan and Neil de Grasse Tyson, and educators, and influencers who can get people truly excited about changing the world for the better.
We must all do our part, especially if you're educated and prosperous. Have a child. Raise them well. Inspire them. Challenge them to be hopeful about the future, and being a part of shaping it.