Well, to use Good Omens' favorite word? Technically lol, the Crowley in Aziraphale's Nightmare was wearing that pretty bra. Every character since 2.01, minus the flashbacks, has been a part of the dream that Aziraphale is having so it's really Aziraphale's subconscious who has dressed them all and, well, hey... remember The Ball? When all their outfits were changing as they came through the door of his bookshop? Yeah, in retrospect, that was another big Clue lol...
So, this Crowley look in Heaven, including the bra? Aziraphale's mind created it. And what is all that mirroring from the story in S1's reality but, well, the body swap, when we saw just how great a Crowley Aziraphale can make. The bra in Heaven in the dream relates to what Aziraphale had Crowley wearing in Hell in reality, and why he did.
Remember how Aziraphale had Crowley taking that holy water bath in a bathing costume? Because he knew him well enough to know that Crowley is actually a lot more private a person than his sprayed-on pants/trousers might suggest? That's what's going on with the bra in the dream, imho.
(Partially. The rest is that it's a whole Crowley-esque bridal ensemble-- so much so that I thought they were getting married when I first saw this look in the trailer. Bride of Frankenstein hair, a look inspired by a going away suit, white lingerie, etc.. It's really because Aziraphale wants to marry his de facto spouse and that is, as Jim summarized in 2.01, a big part of what this whole dream is about-- trying to figure out how to openly and safely be together. When you don't know anything but you know that everything would be better if you could just be near that one, particular person.)
Aziraphale knows Crowley well enough to know how he'd dress. He knows that if he was wearing this Heaven-colored version of his usual ensemble with this virtually transparent top, especially in a situation where he wouldn't be at ease, like in Heaven? Then he'd wear something under it. Some days, that's an undershirt, some days, when he's feeling a bit more midwife than cobbler? It's a bra. On this topic? The "just a private individual" line was one of my favorite puns in S3.
I think this bra would be one that Crowley really would own in reality. It's very elegant and I can tell through the shirt that it's well-made, which he would like. It wouldn't surprise me if this is actually an example of some of his real lingerie. And it's definitely not surprising that Aziraphale's mind would be able to envision that in the dream, as he is well-versed in Crowley's delicates in reality. 😉