If anyone wants to read more about Togashi exploring gender I can highly recommend reading Level E, the fairly short manga he did between YYH and HxH where he lets all the weirdness in his brain run loose and it's awesome. Congrats on finishing the series!!

About the gender conversation: idk what's happening with Kite but Alluka is very clear to me bc Nanika is an allegory for her trans identity, most clearly expressed when Killua basically tells Nanika to go back into the closet for her own safety and Alluka says no she's an essential part of me