LOVE the trans worldbuilding there and 100% agree that giving them a Word for it is the same thing as giving them a Concept for it, and the Concept (as illustrated above) is so much deeper and more interesting. Cultures all over the world have had their own ways of categorizing/classifying the gender spectrum, and those categorical systems are can't really be fully "translated". For example, we can't say that being two-spirit is the same as being nonbinary, because it's not -- it is as much an expression of Native culture as it is an expression of gender. That cultural element is significant enough that it must be considered as its own thing rather than shoved under the umbrella of "nonbinary" and therefore erased.
Now, there has been an ongoing conversation in the fantasy community about, "When is it appropriate to make up a word, and when should we just use the English word?" This is sometimes joked about as The Great Kahvee* Debate (*or other fantastical spellings of the word "coffee"), because of a trend in the 80s/90s for scifi/fantasy writers to anxiously try to erase all real-world concepts from their books in pursuit of Worldbuilding. "Well, you see, they can't drink coffee because they're not on Earth and they've never heard of it," says the Fantasy Writer™, except the drink in question looks like coffee, tastes like coffee, has the same physiological effect as coffee, is drunk in the same contexts as we drink coffee, and is potentially flavored with sukrr (fantasy sugar; spellings vary) and milk from a creature you've never heard of (or, if your author is really unhinged, some other appalling bodily excretion). We have, as a society, mostly agreed that this is Silly, and now characters drink coffee in your fantasy novels.
So the question you face as a writer is, "If this character is [trans, gay, nonbinary, whatever], and it's exactly the same as it is in the real world, should I bother to make up a word for it?" The authors who are answering "If it is the Exact Same, I will use the IRL word for it" have swung the pendulum of fashion on the Great Kahvee Debate allllllllll the way to the other end, possibly out of a desire to do Good Representation. Except... I don't really feel like mentioning a label IS good representation (except perhaps to small babies who don't have enough reading comprehension to recognize a concept unless it is Clearly Labeled), so the way it actually comes across is, rather, a desire to BE SEEN to be doing Good Representation without actually doing much work. Because being queer in your fantasy world ISN'T going to be exactly the same as being queer in the real world. Whatever culture your character is operating within IS DIFFERENT, that is why you have gone to all the trouble to talk about their special magical tattoos or their special magical dragon familiars or their special magical prophecies or whatever. Give them their own word for what they are, IF that categorization system is important in their culture -- and it might not be! In which case they might not have a word for it! Like, a character might just say, "Oh, that man? No, girl, you don't have a chance, he only has boyfriends" instead of "He's gay."
You don't have to give them a label, either a fantasy one or a real-world one. You're allowed to say, "They don't think about sexuality that way" -- that is a perfectly valid worldbuilding choice, and I encourage you to lean into that and explore it! You don't have to have a label! But what you DO have to do is treat your queer characters like whole, complex people and honor the culture that they come from even if it's a made-up one.
Which brings me to the subject of italicizing the special fantasy words -- I'd encourage people to just leave them in plaintext, actually! This ties into an ongoing discussion on the exoticization of foreign languages in English text (link to an article on the subject). Basically, it marks those words out as jarringly OTHER, which 1) doesn't make a whole lot of sense when the speakers themselves are using the words with fluent familiarity, 2) implicitly frames English as the dominant language over all other languages (linguistic imperialism as an expression of white supremacy), and 3) doesn't even make sense from a descriptive-linguistic perspective when you look at how easily and readily English adopts words from other languages into common parlance.
Consider the sentence: "I went to the cafe and ordered a chai latte" -- italicize chai for emphasis is fine ("no, i didn't order a coffee latte, it was a chai latte"); but it is patently absurd to italicize it (or cafe!) for being an ✨exotic foreign word✨. We know what chai is, we know you can buy it at a cafe. The words have entered our language. English speakers are very, very used to learning new words for a Specific Concept ("Sitting in the sauna eating naan and sipping boba that I bought from the tomato-colored kiosk"). Scifi/fantasy readers will do this even more readily (see Jo Walton's article about SF Reading Protocols).
If you're in the dialogue/narration of someone for whom the word/concept is just part of the ambient cultural background, honor that! Even if they are a fantasy person from a fantasy culture, honor it! It's good practice for real life. :)
