Yes, but this is specifically because of the heat death of the universe. It is an inevitable end to everything they care about, that would leave them drifting eternally due to their effectively immortal nature. They gave up because they realised their ultimate fate is either suicide or something much worse, with this understanding coming as a result of the fight that gave them purpose. No other encountered race in the setting has faced anything near that, and the only way to avoid it is to die before it's relevant.
The quest where you read epitaphs from some of them highlights this pretty well I think, there's one that talks about how they fought to leave their planet, how they fought to travel between dimensions, and how they fought for nothing. These are people that will live so incredibly long that the current age of the universe would be a tiny blip to them, they will live to see everything they have ever loved or cared for die, and they have absolutely no way to avert this fate. They give up when encountered with the incontrovertible fact that there is no actual hope for them to change this, no matter how hard they tried.
I'm not aware we're given any information that suggests the Ea were somehow unhappy before they reached this state? The fact that the sundered are not as competent at achieving their goals as the Ea were is why they don't struggle with this same issue, they simply have not advanced to a stage where it's even worth thinking about. The responses we do see from them regarding the topic suggest they're just entirely unequipped to even try tacking the problem at all, outside just refusing to acknowledge it.
I don't think the setting as provided allows for a happy ending in the extremely long term, outside maybe some exceptionally low maintenance immortals just living in giant time travel loops, I guess. Or as some weird suffering obsessed culture that refuses to fix many problems and views their inevitable death as a good thing, maybe, but that's just cenobites crossed with the ancients.
Meteion was wrong because she was (they were?) attempting to take away any autonomy from people or civilisations regarding how they would meet their end, but they were correct about the fate of all life. I don't believe denial of that is a virtue, and I do hope that if there's more quests like these omega ones they might touch more on the Ea, as they're fairly unique in this context.
Personally I imagine I'll die somewhere in my early 80s, or maybe my 90s if I'm unlucky enough, but if you're planning on living past 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 years old I can understand why you might have a different take to me on this stuff.