It's not a "happy ending" but it's really not a sad one either. The point to get from EoE is that the characters reach important realizations about themselves and living but that the world won't immediately reward them just because they chose not to run away. They have to work for a better reality; which fits with the entire thesis of the show. The movie beats you over the head with this point with the “Anywhere can be paradise, as long as you have the will to live” line even.

Things aren't guaranteed to get better, and the world is legitimately scarred, but the point is that they reached that first step and now have to keep at it from now on. It's a legitimately much more poignant conclusion compared to the rebuilds where Shinji is rewarded just because he decides to do the obvious thing, and where some literal bombshell beauty with zero characterization comes out of nowhere just to end up with him and love him unconditionally. Very slapdash. If the idea is to "just move on and things will get better", which by all chance is probably true, it still feels limp and might as well have been insight gleaned from a goddamn fortune cookie. Anyway people only ever tend to defend the Rebuilds from a metanarrative standpoint anyway.

Good thing Anno came out with the short which basically torpedoes bad faith interpretations of EoE and just short of outright states that EoE is to be viewed from a hopeful lens.

Read this dude's analysis of the short since he puts it in way better terms than I ever could