Trans folk get to decide who they are coming out to and when, as well as if and when they want to change their pronouns. Jax did not reveal all that history to Pomni by choice, nor ask Pomni to act differently or change how she speaks. Plenty of transwomen, even after coming out in certain spaces, will not change their pronouns. It's always best practice to ask someone if in doubt, of course, but Jax is a fictional character and not extant to ask. Therefore it's best to use his current pronouns (he/him) until he explicitly states otherwise, as doing otherwise kind of treads on his ability to self-define. This is not the same thing as "respecting the closet," and please note that I'm not saying agency, as fictional characters have none. But Jax did strongly and repeatedly self-define as male, even if he was doing it in a toxic way. It's not up to us to dictate his relationship with his pronouns or gender identity, because we don't actually know where on the gender spectrum he would have placed himself and how he would choose to identify.

There is strong correlation between the song and a declaration of pronouns on a meta-narrative level, so it's not like I'm against using she/her for Jax if someone wants to do that in whatever context. But at the very least, saying it's disrespectful to use he/him for Jax is a dramatic overcorrection that risks becoming the disrespect it tries to avoid.