Spatial audio is a confusing topic because of years of marketing. In the real world, directional audio works through the shape of your ear. When sound comes from a direction that’s not directly inside your ear, it gets modified by the skin and bone, through frequencies being boosted and suppressed but also some reverb. This modification is different for different directions, and your brain can pick up these cues. Software can try to simulate this for headphones, by applying this processing in software, as long as you can “guess” the shape of someone’s ear and then run a simulation of how sound interacts with it. There’s some clever tricks for how to do this very quickly without having to execute physics code.

And logically this makes sense, there’s only one measurement place in each ear, why would you need more than one sound stream going into each ear?

So looking for good “spatial audio” headphones is in my opinion a scam. You’re better off just buying the best audio quality headphones you can without really paying attention to spatial audio.

Terms you might hear online are soundstage (how well you can separate instruments) and imaging (how well software/recorded positional cues are reenacted by the headphones). These two are acoustic qualities that might be important to you.