You're not going to run out of atmospheric oxygen, no matter how much you breathe. There is, for your purposes, an unlimited amount of it.
That may make all your breaths meaningless. But when I'm meditating, or bicycling up a hill, or face-to-face with my lover, or watching the sunrise on a cold morning, my breath has plenty of meaning to me. Limiting the amount of oxygen I was allowed to use would not lend those more meaning; scarcity is not the same as meaning.
> Meaningless for whom or for what? There is no meaning separate from a subject
The philosophical argument for a truly-immortal being being indifferent is that they would, over an infinite timeline, experience every possible experience an infinite number of times. In that frame, preference loses meaning. A being that has no preference is indifferent to what happens around or to them. That, one could argue, is an existence without meaning.
That's so splendidly separate from biological immortality as to be a straw man. (The argument also suffers from failing to appreciate that there are many types of infinity.)
Far from it being a straw man I think it's already a reality that affects us. In very affluent, safe countries we are so far removed from death or meaning that most people's lives consist of picking a different flavor of craft beer or game from their Steam library. This isn't just the concern of some theoretical immortal being, people have a crisis of meaning already, there's a bestseller with that title probably being published every week because in a way the illusion of immortality we have has already rendered most of what we do exchangeable and banal.
Mind you it's no accident that the one meaningful thing most people still have, which is having kids, is precisely given meaning by our own mortality, it's the one transcendent thing that only exists because our lives are finite.
> people have a crisis of meaning already, there's a bestseller with that title probably being published every week
People have always been complaining about this, I think Socrates and Cicero griped about it in their times.
The problem isn’t distance from death but monotony. The philosophised immortal being has monotony forced upon them. Many people today and in the past self-impose it.
How does this cause individual events to lose meaning? Have events that happened to the human race as a whole thousands of years ago lost their meaning?
you've painted yourself into a corner, how exactly are you going to define meaning? As far as we know the universe is infinite, and as such all actions fit your description anyway, so why not be infinite along with it?