I found the source of the issue.
After spending an awful amount of time observing the behavior of "Safari Networking" on the Activity Monitor, I happened to notice that one of the internship portals I added on bookmarks/top sites was constantly causing web traffic by itself.
I suspect it is a bad/malicious domain. I am not quite sure what to do with it (in terms of reporting); but after reseting Safari, deleting all the cookies and taking that intern portal off the bookmarks/top sites solved the issue.