I've tried JabRef, Zotero, and Mendeley. The latter two seem more modern and friendly in some ways but I prefer JabRef. Works well with LaTeX/BiBTeX and it looks more old-school, which I like. Mendeley's advantage is that it has free online storage.
This is probably an automatable task, but it's generally not too much of a burden to do manually. I add a 'needs-review' tag to papers I've identified in a literature review, and categorize it when I get around to reading it.
It is currently in beta but they polished the UI and the UX is now much better than before. If not, I would recommend that you give it a try.
Now if only there were an iPad with a screen like the Remarkable (or a Zotero app for the Remarkable).