Ah, okay.
>What physical purpose does it serve beyond self-actualization, and what makes it necessary for that process in these individuals.
When you say "physical purpose beyond self-actualization" I think you're limiting your own understanding, because people who are openly living their lives true to who they are while being accepted for it by others are more likely to lead happy, healthy, productive lives. In this context, the spiritual and mental purpose is tied to allowing the person in question to lead a happy life here in the world. Personally, I don't think it's worthwhile to focus solely on an abstract "physical purpose" for non-binary people because this is mostly a mental thing, but even then, your brain is a physical object. And I'm not going to get into the well-documented links between mental and physical health.
As for the science behind gender and queerness: I'm not a scientist, I'm a mystic, so I can't really help you there, but here are some starting points for you:
https://cadehildreth.com/gender-spectrum/
https://blogs.scientificamerican.com/voices/stop-using-phony-science-to-justify-transphobia/
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6677266/
https://apnews.com/article/2a67da6515aa48e68e56cd97817b097a
https://www.spectrumsouth.com/history-science-gender-fluidity/
https://www.amazon.com/Genderqueer-Non-Binary-Critical-Approaches-Sexuality/dp/1137510528