For a PhD pursuing a career in academia is a Linkedin helpful? I have seen the other questions on linkedin on the Academia stack exchange page but had a slightly different one.
For a PhD student who is looking to becomes a professor post grad school, is a linkedin helpful?
From what I see, the interview process for academia is the following:

The student gives a job talk at the universities they are interviewing for.
They interview 1-1 with the professors in the department, especially those in the same research field
Their publication record, existing fundings, and CV are reviewed.
Lastly, their recommendations from their own advisor and collaborators are weighed in.

Although point #4 might not be explicitly done, at the end of the day that seems like one of the primary implicit ways a student gets their foot in the door - the student's PhD advisor connects the student to another professor in another university who will vouch/champion them in the interview process.
With all this being said, I see that the academic review board goes directly to the students CV, publication record, and their academic website/page to get a sense of who they are as a academic professional and whether they are involved in the proper outreach activities and support diversity, etc.
In this whole pipeline, I can't imagine linkedin being helpful anywhere along the way. So is it helpful? Or is it only helpful for PhD students seeking opportunities in the private sector? Does having a linkedin affect how I am perceived in Academia?
In my experience (academia and industry), there is very little benefit to LinkedIn in the academic sphere. It just fails to have critical mass in academia, and therefore gets used very little. I'm sure it depends on discipline, but a combination of own/departmental webpage, preprint servers and publication aggregators, and (in some disciplines) Twitter is where it's at. That being said, a low-key LinkedIn profile doesn't hurt, especially if you want to start staying in contact with friends and (former) colleagues who leave academia and for whom LinkedIn becomes a lazy directory of who has gone where and how to stay in touch. I can't imagine it would have a negative effect on perception.
I do however recommend to academics (including advanced Ph.D. candidates) to set up their own, personal (i.e. professionally focused but personally owned, controlled, and managed) webpages, especially if they are in techy- or in any way outreach-to-the-public relevant fields. These days, it is cheap and easy to get a domain name of your own, to set up a WordPress (or similar) site somewhere. Then you get to post your research in the format you want, show a bit of creativity, etc. And by doing it early and well, your site will rank highly in search. It's much more professional looking, to current- and would-be peers as well as to journalists and the public (if relevant) if you have a well-organized and up-to-date website, than if a couple of years down the road a Google Search for you yields 3-4 abandoned pages at institutions you did a post-doc at, with expired links to old papers and no mention of the most exciting topic you are focusing on at the present time. In this day and age you will eventually want to control how you market yourself, and it's easiest to do if you start doing it gently early rather than in a big rush when you discover you ought to have been doing it already.