Background: A little over a year ago, I wrote a paper for an internship (during high school) at a major university medical center. My contribution to the paper was basically everything except conception and some editing/revision (mainly phrasing, not content). The author list, in order, is: immediate supervisor, me, other intern, senior person in group, and PI. The other intern put in about 3 hours of work which were not used in the final manuscript before disappearing to another country and not responding to my attempts to contact. My immediate supervisor, frankly, had very little contribution and is not giving the paper the attention I would like; they took a year to submit the paper (rejected the first time by a reach journal), is taking excessively long to resubmit or get back to me about it, and is usually radio silent.
I have a pretty good relationship with the PI, who seems somewhat aware that my immediate supervisor is not being responsive or attentive. Can and should I ask the PI (or someone) about changing the order of authors; and what actions would be appropriate for me to take to try and get the paper finally submitted relatively soon?
It’s from work done during high school, so I don’t have very much experience with these politics. Thank you!