Given a long enough time frame, the vast majority of an immortal life would be spent buried beneath something or floating in the void of space. Think about it, you outlast planets and stars. When those go dark, but you don't die...nothing to do but float in space.
You might counter that with, "well yeah, but eventually I'd find other sentient life forms and/or people again.” And sure, maybe, but that wouldn't last as long as you...and then you're just alone floating in space again, for the vast majority of your life. The only thing to look forward to, since you will outlast everything, is the end of time itself.
I think there is a clear difference between being immortal and being indestructible. I would think if your planet breaks apart you'd probably die with it being crushed or whatever. Also always unclear if being immortal means you don't need to breathe air.
Here's a sci-fi web novel I read years ago, where a couple of the characters end up being immortal in different ways, and in one case they show exactly how far that can go (in the context of the story) even without invoking heat death.
Think about it, you outlast planets and stars. When those go dark, but you don't die...nothing to do but float in space.
LOL, that's just the beginning -- only on the order of 1012 - 1014 years. After that, you're going to be waiting around for proton decay (1036 - 1043 years), all the way up to 10^10^120 years* for the final heat death of the universe.
(* Anybody know how to get Lemmy markdown to do nested superscripts?)