EoE isn't a happy movie, but it's about happiness. It only states the obvious that happiness and pain are opposite sides of the same coin; there's no promise of a payoff, only that avoiding the coin toss guarantees it'll never turn up heads.
It's more optimistic than it gets credit for. In the beginning, Shinji tells Misato he's terrified he'll keep hurting people he cares about, and that by doing nothing he'll avoid making the same mistakes. Toward the end, he realizes that escaping can never lead to true happiness, deciding to move past his mistakes and engage the world. He becomes self-aware, taking responsibility for his happiness, knowing he's not entitled to it and might not ever find it. He says goodbye to his mother; Yui and Misato and Rei and Lilith are gone, there are no more powerful women to take control, make decisions for him, and protect him. He faces the ruined consequence of his mistakes on his own. For her part, Asuka chooses to leave Instrumentality where being abandoned and replaced is impossible, showing her own resolve to pursue true happiness.
In the end he does the exact thing he was afraid of and hurts Asuka. She replies with a gesture of pure affection; he's not avoiding her, and she's not pushing him away. They're not slaves to their trauma anymore. We don't know where they stand now, or if the rest of the world will return; if we did, the ending would become either be happy or sad, and the nuance would be lost. As Anno once said when describing Eva, contact with others is frightening and ambiguous.
Wanted to look into Anima too, but idk if I will.
Fair warning: ANIMA reads like batshit fanfiction. I love it for that reason, but it's not for everyone.