I've actually never finished a full game of Stellaris. I usually play max-size galaxies, so that might have something to do with it,

That's definitely a strong contributing factor imo. For as many games of it I've started the only one I actually stuck with all the way to the end was one minimum size galaxy fanatic purifier run with a species of adorable butterflies. Any bigger than that and eventually it just hits a point where not only is trying to stay on top of planets a chore but it stops feeling like there's even a point to it since I've snowballed to such a point that I can just brute force whatever's left while slowly waiting for that to finish.

I did have one particularly long running game with an empath tree of life spider hivemind that wound up as the permanent head of a huge federation that also became the sole galactic community security council member and made war impossible, putting the galaxy in stasis with nothing left to do but run out the clock since even the crisis couldn't put a dent in it. That game I played extremely tall (after getting penned in by my loyal allies/federation and some fallen empires) and just relied on barbaric despoliation to capture pops (for livestock) from whoever my federation declared war on to keep my economy growing. I did eventually abandon it once it became a waiting game, though.