Well, that's an interesting project. Extracting data from LinkedIn can be challenging, because of its strict API policies. If you ask me, I suggest checking out Linkedln's Talent Solutions API, but getting access can be challenging. Also, in my opinion, some third-party platforms might help with this.
If you're looking for ways to manage applicants more easily, you could look at platforms like Talentmate for ideas. They offer job posting and applicant tracking solutions.
I wish you good luck with your project.