I'm disheartened that the immediate first response to you is basically "no, humans will be immortal soon enough."

Of course, nothing is immortal. All matter in the universe will eventually be subsumed into supermassive black holes, then spend the next thousands of quadrillions of years slowly evaporating into nothingness via Hawking radiation. I would very much like for my life to be longer than it is, to possibly witness the entire arc of all human civilization, but I sure as shit don't want to experience eternity as undifferentiated non-baryonic matter causally disconnected from all other matter. Death may come very far into the future for certain types of life that don't yet exist, or certain types of information sinks that can act but would not have been considered "life" by existing biological definitions, but it will still come, and if you live enough, it will be welcome.

Personally, I take a lot of comfort in this. Not a single one of us, not Charlemagne, not Khan, not Elon Musk, matter any more than an amoeba in the truly grand scheme of the cosmos. Even a hypothetical type III civilization is just as much dust as the Mayans in the long run. Conversely, within our own little sphere of influence, we all matter as much as a god.

I get why life has this ambition. I feel it, too. It's the reason we exist in the first place. But we're able to recognize it for what it is, the illusion of an imperative handed down by semi-random behaviors selected for no better reason than they made it more likely for their associated genes to proliferate. There is no actual imperative. That frees you to live within the confines of a tractable life of tractable ambitions. Be the absolute best person you can be to a small group of sentient creatures you happened to exist alongside for somewhere between a few decades to a century. Don't set the planet on fire and neglect your own family in an attempt to become a comic book hero.

I don't care about absolutes.

Give me 500 years of life with good health and I will be more than satisfied.

You might want to read Cordwainer Smith's take on immortality, such as "The Rediscovery of Man."