Speaking as a neurodivergent person who is very strongly on the autism spectrum, Nemona just comes off to me as someone who is very much neurodivergent (which I found relatable when playing Violet), ie very much showing characteristics of a neurodivergent person.
She has an extreme love for battles, to the point where it's an extreme passion and hyperfixation for her in a sense, which is something I can understand fully well. Battling is her life passion, and she shows it in many ways, including how she looks up to Geeta (La Primera), the head of the Paldea League and the Top Champion, even after she herself claimed the title of Champion.
She also has a habit of being so overindulged in her hyperfixations that she tends to not read the room very well socially, which is very evident during the final Area Zero storyline where she's very excitable and still all about having fun while Arven and Penny are more serious about the whole thing, and her overt energy puts Arven and Penny off from her at first and it takes a while for them to get used to her. Even before this it's pretty well established early in the story that Nemona and Arven know each other but fundamentally are on such different wavelengths that they can't stand being in each other's presence. With Arven you can very clearly tell he doesn't really seem to like her very much at all.
Her schtick is that she's in a very prestigious position in Paldea in many ways, coming from a wealthy family (they practically live in a mansion), she's the student council president at the esteemed Naranja/Uva Academy, and she's a Champion Rank Trainer, in other words she's one of the strongest Trainers in the entire region. But despite having all of that, she's actually lonely deep down because she doesn't have many friends. Not many people truly understand her because she doesn't know how to make friends, and many people don't feel they can be close with or be friends with her due to her prestigious position, basically establishing herself as above them socially in many ways so no one really sees her as an equal or is willing to try to get to know her because of that disparity in perceived social standing between her and them. Further reinforced by her general tendency to...not read the room with others a lot of the time.
Her storyline, which culminates in the final battle between you and her at the very end of Victory Road, tying in with the player, is ultimately finding a fellow Trainer and battler that she can call a true friend, a true equal. And you, the player, are that person who can be that person who stands on an equal playing field with her. From the moment the player moves into Paldea and in Nemona's hometown she has hope that she can get to know them better and find someone who is actively willing to get to know her and be friends with her. She's actively rooting for your success as you pursue the Gym Challenge, and looks forward to seeing you continue to get stronger, and ultimately she hopes that you can ultimately become strong enough to be her equal.
And it finally comes through after the player passes the Champion Assessment and becomes Champion themself, culminating in a climactic battle between the player, now a Champion, and Nemona, also a Champion, and the player winning. Nemona finally gets a battle that she can truly enjoy, with someone she can call a friend, and who is on equal footing if not even better than her as a strong Champion Rank Trainer. A battle that finally allows her to all out, full throttle, with her full strength and holding nothing back (worth noting that it's strongly implied that Nemona was holding back her true power against Geeta when they battled). Someone who is a friend to her, who shares the same passion for battling that she does, and is therefore on the same wavelength as her. Which is why that final battle means so much to her: both the player and Nemona share that passion for battling, are both Champion level Trainers, and can go all out against each other holding nothing back: Pokemon battling in its purest form.
Paldea's quest involves the "Treasure Hunt", which means all of the students journey through Paldea to find and create meaningful experiences. Yet as the player, one can find the most fulfillment in helping others find their treasure. Which is what happens with all of Arven, Nemona, and Penny's storylines and arcs, especially when they culminate and intertwine in the final No Way Home storyline.
Nemona finds a true friend she can see as her equal and shares the same battling passion and strength as herself, but ultimately all three of them come together around you, the player, and the four of them become a close knit group of friends who are close with each other, because they all found what they valued most in their life because of the player.