I think somewhere around that age is when a lot of folks start noticing how many “last times” for various experiences are piling up, and that a ton of their remaining experiences are also going to be “last times”. It’s when you realize you’re in a slow-motion process of saying goodbye to life.
I'm not an example of anything, but it happens that I was concerned about mortality from about age 7 - not frightened of it, but indignant. This should obviously be the most urgent concern for everybody, yet we do nothing about it, I thought. Before I decide what I'm going to do with my life, I'm going to fix the problem of it ending way too soon. But as it turned out, I would rather die than study molecular biology, so now I just vaguely hope somebody else will fix the problem.
Humanity's earliest surviving major work of fiction, Gilgamesh, is largely concerned with this. Ancient Egyptian literature is obviously full of these concerns, and you can keep on going down the list of ancient civilizations with surviving literature, it's always there. Worrying about this, wishing to find a solution to this problem, and even working at it (and, always, failing) is about as human as anything can be.
The good news is that we are probably a few decades away from robust rejuvenation, that will allow us to live more or less indefinitely absent catching a disease or meeting with a horrible accident or something. In the next 20 years or so we have a very good shot at a first wave of treatments that will extend our quality lifespan to where we will see the next wave, so-called "longevity escape velocity".
And yes, this is an ancient, ancient dream of mankind, one replete with cautionary tales about the Bad Things that will befall you if you attempt to actually solve it. (One such tale, The Substance, was nominated for a few oscars.) But so was human flight. We yearned for it, and our elders told us what fools we would be for even trying with things like the tale of Icarus... and then one day on a hill in Kitty Hawk, NC...
tales against flying? you forget daedalus who made it out just fine sans a son. icarus’s problem was that he overstepped his limits, not that he dared to fly.
from what I’ve seen tales against a search for immortality are in regards to enjoy life while you have it, make relations, laugh, love, mourn, and remember, rather than have your entire life consumed in a desperate attempt to postpone the end, sucking all the joy out of it. we still have a long ways to go to avoiding death entirely, so I’d figure the best course of action is to enjoy life rather than to waste it in hopes of getting some extra time.
Of course the body is not the same. Time is more precious. But that really doesn't mean your margin of error is smaller. When I was in my twenties I had a lot less margin for error. Failing a test could mean the end of my degree. Not finding a job meant I could not pay rent. This is even worse for some other people. Imagine not getting accepted into Harvard because your letter just not being good enough slightly. If I fuck up my job now, the worst that can happen is that I get fired. I have enough financial means to support myself and find a new job. There is a ton of risk I could never take as a younger person. Precisely because now my margin of error is much larger.
There are, of course, also examples where the converse holds true. Finding a long term partner who you want to create a family with for example. But all in all the balance strongly favors that the error margin becomes smaller.