If the entire galaxy is dead as Mars, what do we even have to strive for?
The next galaxy over. Repeat until something useful is found. Our current understanding says the universe is infinite. Ergo there is always somewhere else to look.
Best case being a shitty expanse like existence where we struggle to hold on to a miserable life in a space that doesn't want us there at all for no other reason than to mine dead rocks off of bigger dead rocks?
That's a "pragmatic," arguably very Russian attitude towards space exploration. Reasonable, guarded, cautious, and completely reasonable and respectable. Not sarcasm. The Russians didn't win the race to the moon, but they still sure as shit know how to build a working spacecraft and a working rocket. They put in the same blood, sweat & tears we did and they earned their wings just as hard as we did. And (undisclosed secrets notwithstanding) they've lost fewer people to their space program than we have.
The classic American attitude towards the same statement is: "space that doesn't want us there at all? Fuck you space, we're here anyway and you're ours now. We will conquer and explore you or die trying and we'll fucking take you with us if that's how it's gonna go." As much as I hate ever evoking a politician, Kennedy's moonshot speech included the classic line "We choose to go to the moon in this decade and do the other things, not because they are easy, but because they are hard." Literally "someone said we can't or shouldn't, so fuck 'em, we're doing it." That's powerful. It's also true. And BTW we did it.
What's that other classic joke about the difference between the Americans and the Russians in how they developed their space programs? "They needed to write stuff down in flight, so NASA spent X million dollars inventing a pen that could write at any angle in zero gravity. The Russians took a pencil." We both solved the same problem differently -- one with innovation (that eventually trickled down to every day life like most space program stuff does) and the other with pragmatism and practicality (not spending time, money and resources they couldn't afford, when a natural alternative was readily available).
I think intergalactic exploration will honestly require both attitudes working together. We Americans bring the cowboy arrogance, crazy-ass ideas, high technology and autistic determination and enthusiasm, and the Russians bring their wealth of experience and their natural pragmatism to counter-balance it with their general attitude of "well, shit's fucked and/or this might be incredibly stupid, but fuck it, it's gotta get done and we're already here and running out of air, so we might as well start MacGuyvering shit so the alarms stop buzzing in our ears and we don't die."
The one thing that truly encourages me most about space exploration is how the politics of it tend to stay on the ground (for the most part). I'm sure there are personal squabbles on space flights and on board the various space stations over the years, but every indication shows once a crew (of any composition) is up there fucking around in zero-G, they tend to consider themselves "team Earth" and not "team America vs. team Russia vs. team China." Lest you accuse me of espousing a pro-globalist leftist ideal, it's not that the borders aren't still important or that individual backgrounds don't matter, it's just more the fact that on that kind of "micro" scale in such a macro environment, the distinctions aren't quite as important as making sure you'll still have air to breathe and food to eat in an hour.