I can try. If the result of doing something vs doing nothing is indistinguishable after a certain time, does it matter that it ever happened?

Turn it around. If the result of doing something vs doing nothing /is/ distinguishable at some point in time, does the choice matter? Yes, it does at some point. Granted: it doesn’t matter at /most other points/ in time, sure. But it’s something.

That's a good question, and I'm certainly not trying to suggest that there exists a right answer.

My thoughts are that the formulation assumes the perspective of an observer outside of the system, treating the system as a sort of black box, waiting for the system to produce some sort of signal. And because our current understanding of heat death means that the "signal" will always be something indistinguishably meaningless, the outside observer (who cannot inspect the inner workings of the system) is free assume that, from their perspective, nothing of meaning occurred inside the system.

But even if we assume the above to be true, this is still compatible with an alternative interpretation: from the perspective of an observer inside the system, we may distinguish differences in the system and may find meaning in those differences. Although that's "may find meaning", not "will find meaning"; determining the meaning of one's existence is intensely personal. However, given the above axiom, I don't believe it precludes finding meaning.

Why wouldn’t it? I feel like things matter MORE when they don’t last forever. If something lasts forever, then each moment isn’t important, because you will have infinite more moments of the same thing. Only when something is limited does it have specialness.

It depends on your perspective. If you experience time as a spacelike dimension, you can look at this part of spacetime and be amazed at the rich tapestries we, the weirdos who perceive time as timelike, weave with our lives.