I see lots and lots of advice on here and other forums, but I'm curious if anyone has ever done any actual research on learning chess? (i.e. do you know of any scientific research, published studies, etc.) How do people measure "success" and "improvement" in chess?

Most of the advice I find seems like it is hugely suspect to survivor-ship bias. A lot of the advice is banal and borderline meaningless (e.g. stop blundering)

I've been playing online off and on for a 18 months or so now. I like to watch a lot of instructional videos (e.g. "climbing the rating ladder" by John Bartholomew or Daniel Naroditsky). I catch a fair few streams of high level tournaments (usually with commentary). I play a mix of slow rapid (15 10) and bullet (1 1/0 to throw pieces around). I use openingtree and every few weeks go through my games. I'm always hoping to see some glaring weak spots, but usually I'm right there at 45-55% win rate in all my openings. I have gotten a copy of a few books (e.g. Michael Stean's Simple Chess which I have found anything but simple). I do lots of puzzles on chesstemp and lichess (including dedicated "theme" sessions). And for the past couple of months my rapid rating has plateaued (to be expected, won't always be improvement) and my bullet rating is basically in free fall. All this got me to thinking if my "study" time is well motivated.

I don't mind being bad at chess. I enjoy things that I can work at and improve, but I generally don't enjoy things that I get worse at despite putting in work. An analogy I often think about is running (or most exercise really). I might be a slow runner (bad at chess) who has absolutely no delusions about being a professional marathon runner (GM), but I can go out every day and run. If I work at it, I can run faster, farther, longer, etc. and see improvement in one or all of those areas. There is also a whole ocean of terrible advice out there on "running tips" and "running training strategy", but there is also actual research I can read. There are also lots of simple ways to mark progress and improvement. Does anything like this exist in chess?