Recently an article was published regarding Spelljammer and what items or races could be used to survive in the airless confines of realm space. Amongst the items, the Necklace of Adaptation was not listed. The item allows you to be able to breathe in any environment, so wouldn’t that allow you to survive in the airless parts of space?
A Necklace of Adaptation does, indeed, allow the wearer to "breathe normally in any environment". This GM sees no reason to believe that it wouldn't allow the wearer to breathe normally in the airless parts of space (or airless parts of planets; ie., under water), nor can I see an interpretation that would preclude its use.
My supposition is that the necklace is a well-known item (it exists at least as far back as 3.5, which is where I started playing); as such, it's a fairly obvious solution - for players with a high degree of system expertise - to the "airless" problem. It's also a straightforward solution where the article, if Thomas Markov's comment is correct, focuses on less-obvious options (a friendly plant creature, petrification, and a very slightly cheeky reading of how a cap of waterbreathing and a bucket of water interact). That is: the list isn't meant to be exhaustive, but to remind players that there are options other than "play a race that doesn't need to breathe" and to think outside the box for those solutions.
... says the player rocking a 3pp not-quite-Warforged in a Spelljammer campaign that's just started, not least because of the whole "doesn't need to breathe" thing they get ...
Technically, you're never exposed to vacuum in Spelljammer.
In Spelljammer, objects in space hold an envelope of air around them, and the size of the envelope is based on the mass of the object. That's how you can have spelljammer ships that aren't airtight; the air just sort of sticks to them.
The same holds for a creature that falls off a ship. They take a little bubble of air with them, and if not rescued, the air will become unbreathable in a short time. They'll eventually suffocate, but the body will still have a little cloud of what the rules refer to as "foul" or "deadly" air (but what we would call carbon dioxide) around it. I'm sure there are extraordinary circumstances where the normal rules don't apply and you can end up out in raw vacuum, but that's not how it generally works.
Under normal circumstances, whether a necklace of adaptation would work in the void of space just doesn't matter, because it would be the bubble of increasingly foul air around you that it allows you to continue to breathe without ill effects.