There is no difference between the rights and duties of a PhD student doing their first review or a professor doing their 1000th.
You're free to tell the fact that you got a paper to review, and which journal that request comes from.
You are bound by the reviewer guidelines of the journal in question, like any other reviewer.
Unless they explicitly state that fresh PhD students may do the
review with the help of their professor (which I'd consider extremely
unusual), you cannot disclose confidential information, e.g. content of the paper, to your supervisor.
In my field, we have such confidentiality requirements regardless of whether a preprint of the manuscript is publicly available or not. If a preprint is available, you can discuss the merits of the preprint as it is publicly known with your supervisor, but then cannot not disclose the fact you are reviewer for that manuscript.
You may ask your supervisor (or other colleagues) general questions, though.
Say, you find a dynamite plot "summarizing" 5 data points each into a bar and standard error - and wonder whether requesting the authors to change it into a point diagram is OK or asking too much: by putting the question in such abstract terms you do not reveal the content of the manuscript.
If you feel you are not fully qualified to do the review without asking colleagues (e.g. your supervisor) for advise about the content, that is typically possible by contacting the journal editor who will then give you leave to talk e.g. with your supervisor.
When I received my first review request, I told the fact at lunch break, and that I did yet feel qualified to judge a manuscript. My professor told me to please remember that I'm a fully qualified chemist since I graduated with my Diplom (nowadays Master), with all professional rights and duties that come along with it. And that papers are supposed to written so that they are understandable and the argumentation sufficiently clear convincing to any professional of roughly the (sub)field in question. In other words, to people like me.
IIRC, there was also an argument that already my Diplom thesis required me to critically judge the papers I studied wrt. what conclusions can be drawn from them.
Nowadays, I'd say: if a supervisor thinks their students need direct training on how to write a review, a format like a journal club is a very good opportunity to do so: the papers can be openly discussed to their merits in a group, and also what can reasonably be requested and to formulate this can be developed with a whole group of students. And this is possible without compromising a review process.
BTW, I suspect that I got this review request either because he as editor of the journal (of which I was not aware at the time - IIRC I did not see who the editor handling the manuscript was) suggested me or because he suggested me as alternative reviewer when he turned down the review request.