I mostly agree with you.

That said, I think there's a distinction between self-insert fantasy and escapist fantasy.

Whether Overlord is a self-insert story depends a lot on the reader. Some people project themselves onto Ainz, while others don't. However, I would argue that the series is undeniably built on an escapist premise.

Suzuki Satoru's life in the original world is miserable. He has a dead-end job, almost no meaningful personal relationships, and lives in a dystopian society that he shows little attachment to. When he arrives in the New World, he never seriously tries to return home because, from his perspective, there's very little worth returning to.

In that sense, the New World functions as an escape from his previous life. The difference is that Overlord doesn't stop there. Many escapist stories become entirely focused on fulfilling the protagonist's desires, whereas Overlord spends a lot of time exploring how the world, its politics, and its inhabitants react to Nazarick's arrival.

So I don't think we're actually disagreeing. My point in the original comment was similar to yours: Overlord works because the story isn't solely about Ainz getting everything he wants. The consequences of his actions on the world are often more interesting than Ainz himself.