I see this story has continued down the same path it started. I decided to skim another chapter or two thanks to the yuri tag getting added. To each their own. This isn't for me.
As for trans people being mentally ill it is simple fact at this point since gender dysphoria is listed in the DSM 5 aka the book that contains the world's consensus on the diagnostic criteria for mental illness. It is literally the book that defines what is and is not a mental illness.
It is literally the same book that defined homosexuality as a mental illness in earlier editions. It is fallable.
Aside from which, being trans is not presently defined as a mental illness even in the DSM, the discomfort of dysphoria is the issue dealt with there. And that, in part, is because in many places you can't get treatment paid for by insurance unless you have a diagnosis to bill it under.
Not to mention* trans people are constantly barraged by messages from many directions who aren't medical professionals calling being trans (plus other gender variance) itself a mental illness as a way to belittle or invalidate their experience, so you can kinda see why there'd be a wee bit of resistance to seeing that carry over into fiction.