What's a polite way of confirming if a position offered is official?
I was told by the PhD that if I'm to accept, she will have to seek permission from her PI / keep the PI in the loop - which makes me feel that it's probably official but I'm not sure.

The PhD student likely has no authority nor budget to hire you. They're trying to establish whether you'd take a position if formally offered. If you will, they'll go and get permission/money from their PI. Whether the PI will hire you depends on the PhD student's sway with the PI and on the PI's budget.

What's a polite way of asking for the necessary clarifications?

TL;DR: Say, I'm interested, how do we proceed?