That story sounds absolutely incredible and interesting and I'd love to read it. It's a much neglected fact that one, intersex people can be transgender and two, someone might realize they are transgender because they are intersex or their transgenderness and intersexuality are uniquely or inherently connected.
Thanks for the compliment
My only or main feedback would mostly be how you are conceptualizing their intersex variation, specifically on how you say their female parts are fertile but their male parts aren't (which is realistic, people are rarely if ever fertile with "both" if they have "both"), so how exactly are you visualizing this? Do they have those parts internally without being able to access them and are fertile with them, etc... I recommend researching or choosing a real intersex variation and sticking to it (Müllerian duct syndrome sounds like what you're describing, or closest to it). I don't see anything wrong with varying from it a bit because not everyone IRL nearly fits a variation's "criteria", but I would make sure you don't like, over-fantasize it and make it realistic (which it sounds like you're doing)! It seems though like you're probably already aware of this, but I just wanted to make sure.
It is Müllerian duct syndrome basically. In the story this condition is sex-linked (like hemophilia), where the female is a carrier (Xx), and the carrier's sons have a 50% chance of being affected by it (xy) whilst daughters have a 50% chance of being a carrier (Xx). Affected females are the same as carriers except there's a 100% chance (xx) their daughters will be carriers and their sons will be affected (xy). Affected males have those parts (uterus, ovaries and part of the upper vagina) internally without being able to access them and are fertile with them. Much like real-life Müllerian duct syndrome, most of their male parts are infertile.
The only other personal tidbit I can think of is, if being trans+ is incredibly widely accepted, I find it super interesting that being intersex is maybe less accepted, because concepts like AGAB and a gender binary still exist in this world. You could either consider that and how to address that or use it to your advantage to make a stronger point on intersexism or intersex experiencs—just something to consider. I am a purveyor of fantasy-based homophobia, transphobia, etc, and really enjoy considering how sexuality and gender exist in a certain fictional world based on the pre-existing worldbuilding of their gender and sexuality roles, if that makes sense.
I will say this, given how commonplace gender reassignment is (1 in 10 of the galaxy's population had a gender reassignment operation), LGBTQI+ stuff (yes I include intersex people as part of it) would be normalized. Ofc there are a number of people who are homophobic and/or heteronormative but such people are usually seen as backwards and behind the times. That being said, this normalization is not uniform. Some parts of the galaxy are more accepting, others less so.
Maybe some people might feel that it could be saying intersex people must be trans or can't be binary or cis, but that is definitely not what you're saying, so maybe be aware of how some people think that and make it clear your character is going on their own personal journey. Especially since because trans intersex people do exist and we deserve to have our stories told and shown!
It is definitely their own personal journey. As I said earlier, the doctor was stunned that the main character chose to get the gender reassignment operation to become a woman over getting a hysterectomy and testicular transplant, implying that the doctor has dealt with such patients and they all went for the hysterectomy and testicular transplant so they can continue living as guys.
That being said, later on in the story (when the main character has her first menstrual cycle), the main character confides to the therapist some more reasons why she went through the gender reassignment oepration upon finding out she has female reproductive organs and that her male parts are infertile but her female parts are fertile. If you wanna hear those more reasons why be my guest.
Thinking more on it, the only other thing I would be careful on prior to the new info you gave me is making sure it's clear that she is getting SRS because she WANTS it and NOT as an intersex correction, because it could easily accidentally draw parallels to that (and I know that's not what you're doing, but someone could interpret it that way).
I'd also be very careful in how you portray her "girly girl" side. It is absolutely okay for people to be like that, whether they are cis women or trans women, but it could be very easy to either take away the message that she must be that way for her to correctly transition or that she is doing that out of societal pressure rather than her own wants. I would make sure to balance portraying her femininity realistically and genuinely. That they are things that she likes because she just likes them, and not because they are necessarily female-associated. Some ways to maybe balance this out would either be through her own internal narrative exploring why she likes these things or if it's forced, other characters being concerned, or addressing the fact that she so suddenly jumps into the realm of things that are "female" after having not for so long (which is actually a very common thing for some trans+ people, which is something that often does bring up that concern of friends or family after the person having had no signs before). (Also, genuine question, what is girly running?) But yeah, it's absolutely okay to have someone be a feminine or incredibly feminine or "girly" character, whether or not they're cis or trans, but it can be important to take care in portraying it realistically and considering why a character likes those things and why you, the author, have come to the decision to write the character with those things.