The only conclusion that seems even remotely supported by the evidence here is that writing by hand is important for learning
letters. As in, learning your ABC's. No arguments there.
The new study cited is a Norwegian small-sample-size study of college kids typing vs. writing Pictionary words while wearing an EEG. Not learning, I would point out.
What they observe is more connectivity between brain regions when they write, because well, writing and uses more of your brain. And then they make this immense leap to, "and it seems like the connectivity we see when people learn, ergo it's good for learning."
Then Scientific American amplifies it because it's a divisive non-falsifiable thing that people (like me, admittedly) get weirdly invested in. This is bad science and bad science comms. Show me how you decided that this connectivity pattern was evidence of learning when observed in a non-learning context—that's the crux of the issue.
I suspect you can't "see" learning of the type that college kids do in an hour-long EEG session. It unfolds over days, months, years.