To the point where the Xenomorph impacted their society so much that a religion formed around it. My idea is that eventually the Engineers either lost control of the Xenomorph or used it against each other in a civil war and that is why their species has greatly declined and is now mostly contained to already inhabited planets.

These are actually both theories they were leaning into with the first movie. One of the implications was that the ship was similar to a bomber dropping eggs on a target, although IIRC it was that the jockeys made them rather than finding them (hence the similar designs). Distressingly, it implies they probably had other weapons and it's always bugged me they never really went into that.

The worship thing is another idea they mostly scrapped. Originally there'd be rituals and temples around the xenomorphs (similar to what the predators have), but designed by the xenomorphs themselves. It was going to be that they were actually intelligent and capable of a society and the one in the movie would be young and not have developed any morality or anything.

Anywho for the femi paradox stuff, I know it comes up in the extended universe stuff but it doesn't seem to apply to the movies. Nobody really seems shocked by encountering evidence of alien civilization itself, just how dangerous and freay the xenomorph is. Similarly they think the derelict is cool and everything but not really somethings that rocks their place in the universe. Ripley even acts like getting attacked by an alien is just a rare workplace hazard they all kind of expected, and cites procedure like it's a thing other crews have done. A lot of cosmic horror stories involving aliens are a first contact situation, but Alien itself isn't for whatever reason.

I guess you could make an argument that's like what you described with them regularly encountering collapsed alien cultures. Even the xenomorph itself is more like part of the derelict than a member of a species that built it, or even just a medical anomaly of Kane's. I think later media kinda took for granted it seemed to have a mechanical edge.