Use of 'enjoy' with respect to a status or position without pleasure?

Enjoy: To have the use or benefit of; to have something as a benefit or advantage; to benefit from.

Those meanings of enjoy answer your primary question, and show how the word can be applied in several generic situations. Still, you've done a great job of digging up some quotes that use the word in a rather odd sense (most especially, "enjoy refugee status" – that sounds like an oxymoron!).

While I acknowledge there's no grammatical error, I examined your quotes, and wondered how I might reword them. The best substitute for enjoy that I could come up with was benefit from, i.e.:

[...] the film enjoys temporary status as a new release.
[...] they are recognized as a "refugee" and enjoy refugee status.

become:

[...] the film benefits from temporary status as a new release.
[...] they are recognized as a "refugee" and benefit from refugee status.

Maybe the authors simply preferred to use a single word? (Other than enjoys, what's a single-word verb that means benefits from?)

Again, there's obviously nothing wrong with it, but it's still a bit curious nonetheless.

To enjoy a status is to hold and benefit from it—we take pleasure in what’s good for us. The word has lost some of its original sense of benefit and pleasure, I think in part because it is so often used with status and position in a generic sense, but also thanks to advertising: Enjoy Coca-Cola!

We say that someone "enjoys" a status or position meaning that they find it desirable. I don't suppose that someone "enjoys temporary residency status" in the same sense that one "enjoys a candy bar", i.e. that it makes them feel good and they may sit back and savor it. But the ideas are clearly related: In both cases -- the privileged status or the candy bar -- the person gets some benefit that they are glad to have.

Note that if someone "enjoys temporary residency status", this implies that the alternative is being deported, or something else that is less desirable. If you expected to obtain citizenship but were turned down and told the best you could get was temporary residency, you wouldn't describe yourself as "enjoying" that. You'd say that you were disappointed that that was all you could get. (Well, you might say you enjoyed it in the sense of making the best out of what you got, like, "I applied for citizenship and was turned down, but at least I can continue to enjoy my temporary residency status.")