Full Disk Access is a user privacy setting. App Review can't give that to your app. Only your users can give your app Full Disk Access.
Furthermore, Mac App Store apps are sandboxed. That's a separate layer of privacy protection. You have to ask the user to give your app access to a given folder (or root) and then the user would also have to give your app Full Disk Access.
Technically, it is possible. A few years ago, I had an app that did all that in the Mac App Store. I don't remember the relevant App Review communications at the time, but I remember thinking that I was not allowed to ask for Full Disk Access or direct users to it. I had an option in app settings to provide it, but users had to find that on their own. I could give them instructions on the web site, but not inside the app itself.
I can't say what App Review's current policies are. All I can do is relate my own experience. I would also suggest that you're entering into a dangerous area. What kind of data from third party web browsers are you looking for? That's a suspicious Big Red Flag. Merely asking for such access can trigger a closer look at your app.
You might ask, "What's the worst that App Review can do? Reject my request?" No. The worst that App Review can do is kick your app out of the store and you out of the developer program. Apple has over 51 million developers. They don't lose any sleep over terminating 100-400k developers per year. And the #1 category for app removals is "utility".
You're talking about a Mac app. How much money are you really going to make from it? Even if you succeed, it's a horrible user experience.