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?

I don't actually know what "official" means. If your institution has some definitions for such things then it makes sense, but people can't normally just make up titles for things. They can, of course, provide letters in which things are described informally using words that sound like titles. But "official" depends on some institutional backing.

But the way to learn is just to ask, not worrying much about "polite". Will you have a title of some kind that you can use on your CV? That is the question you want answered, and if, no, ask how you can/should present it on the CV.

But you are wise to want to have it clarified. Even if it isn't "official" it can be a good thing on the CV.