Not sure how OP knows about the specifics of Ad Astra's director's cut, since it doesn't exist. At least not yet. Look at what James Gray, the director, said about the matter in an interview for Vulture (late 2022):

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>Q: Is there any chance we might see a director’s cut of Ad Astra?

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>J.G.: I’m going to need help. It’s a lot of money to do it, probably about 300,000 bucks. The question really is this: Is there a way to monetize it? I would love to do it different. The director’s cut is 12 minutes shorter, by the way. When is the director’s cut shorter than the released version? But there is somehow more Ruth Negga and more Donald Sutherland in it. There are other things that are much shorter. But I’d love to do it.