According to the OP article Manning entered the military in order to "straight"-en himself out, having self-identified as "Breanna" and dressed in women's clothing and makeup prior to enlisting.
I think this kid has a basket of neuroses that he mistakenly thought the rigor and discipline of military life would take away. He's obviously been deeply troubled for a long time, and got so wrapped up in his pain that he thought a document dump of classified info would be the right thing to do.
I don't think he should get either hormone therapy or sex reassignment on the taxpayer dime. Neither has anything to do with his health as a prisoner, he has no social life in prison to speak of that would require him living as the sex he thinks he truly is.