>How can we cope with this

I think society needs to start caring more about knowledge integration. At least papers that are published by journals (not preprints) should more often be put into context and made useful by integrating them into existing knowledge systems at the right places.

That's what I'm trying to do when editing science-related Wikipedia articles (along with my monthly Science Summaries that I post to /r/sciences), updating them with major papers of the year (that also includes the much-expanded article applications of AI). I would have thought somebody took care of at least the most significant papers.

It probably needs more comprehensive overview- & context-providing integrative living documents that help people make sense, properly discover and make use out of the gigantic loads of new science/R&D output beyond Wikipedia.

>AI itself can help, by predicting & suggesting new research directions

I think many make the false conclusion that AI is the solution to such problems not a help to a (small) subset of those. Suggesting new research directions seems like an interesting application.

Many ways that could be useful would only be software, not AI. For example, it would be great to somehow better "visualize" (literally or similar) ongoing progress / research topics/fields or categorize papers by their research topics so you can kind of get notified when new subtopics emerge or new research questions related to your watched topics/fields get heatedly debated/investigated etc or auto-highlight text to make things easier to skim etc. I've put some of my ideas (related: 1 2) for such to the FOSS Wikimedia project Scholia which could integrate AIs.

Here are some more similar stats about papers (more CC BY images welcome). Example: ArXiv's yearly submission rate plot

>I have about ~100 open tabs across 4 tab groups of papers/posts/github repos I am supposed to look at, but new & more relevant ones come out before I can do so. Just a little bit out of control.

See some ways/tools to deal with this in this thread at r/DataHoarder here

More R&D (studies, addons, ideas, ...) about such could be very useful as it could accelerate & improve progress on a meta-level.