When I started using it I thought about it like a "Second brain" in the sense of it would somehow make me effectively smarter. I imagined referring back to stuff I'd written, building connections, and the notes letting me discover or recall insights I may have missed. Instead, like the author of this piece, I find that most of the benefits seem to come from inspiration and overcoming inertia and I almost never refer back to things I've written in the past.
The inspiration is usually simple stuff, like if someone told you a problem you might immediately react with a solution or question. Same kind of thing happens when you write out problems. For example, recently my wife was annoyed at me because I haven't done a chore I said I would. As I'm just jotting this down into my daily journal I have the obvious "Why don't you take out the boxes now?" question. I answer that now I don't want to do it because she scolded me and I don't want to reinforce her scolding me. As soon as I see those words, I realize that's childish and I go take out the boxes.
It's a realization I might not have confronted had I just existed in a non-reflective state. By typing out what's going I gave myself the chance to make conscious questions and observations which I can then react to. Sometimes they are useful.
Journaling also helps overcome inertia. Left to my own devices I might spend all day on hackernews, Twitter, YouTube, and taking care of kids. When I journal though I document my frustrations with living that way and that helps push me to work on my side projects more.
Further, just the act of writing things out helps me get started. If I have this nebulous idea that I want to work on "an idea" it's hard to actually start doing it. Decomposing a big idea into discrete chunks is inherently productive - it's drafting a plan and thinking through the system end to end. When I've written out a plan I have something specific and actionable to work on and my mind is already in the "Work on X" state.
Note taking has also helped with ideation. Last night I wrote that I wondered whether Spotify would ban Joe Rogan and challenged myself to predict whether or not they would. While I was writing a brief argumentative essay to myself making my case (low confidence they do ban this year) I came to hold an opinion on Spotify the company (long straddle). I was then able to queue up a buy order - which I wouldn't have done had I not been note taking. (Although, whether or not this idea was good for me remains to be seen)