@IsaVulpes:
Your posts raise many interesting questions. Unfortunately I'm pressed for time now, so I will have to be a bit brief: [
Edit: Yeah right, as if I'm able to write briefly on a topic of interest! Now I'm logging out for the day though ]
I took a look back at my own notes from the Chess Exam, and I also scored 200 points above my actual FIDE rating. One thing I noted was that three of my known weaknessess at the time were hardly tested at all in the book: Time trouble, taking it too easy against lower-rated opponents, and strategic endgames.
It's very hard to say why you scored better on the test than your actual rating without more information. If you're not doing it already, try combining the Lichess analysis with writing down your thoughts and the lines you looked at during a game. Ideally you should get this down in a database or on paper before you touch an analysis engine. Then you can look at your thinking process in all the positions where you lose significant eval and compare it with engine suggestions (or suggestions from other players if possible). Look for systematic patterns. Are you missing the same kinds of themes or moves over and over? Is there something in the thinking process that goes wrong more than once?
Neither "practical skills" nor "failing to convert won positions" are simple problems; you need to break them down into more specific issues you can work on. And the only guide to that is what you were actually doing and thinking at the board, especially at those points where you lost a lot of eval.
I know when I fail to win a won position, it's often because of relaxing a bit and getting careless; the very thought "now I must be winning" is simply very dangerous to my focus at the board. But it could also be about not seizing tactical chances, making wrong exchanging decisions, especially into endgames, misplaying strategic or technical endgames, not being good enough at attacking play or calculation, etc. With your test score in mind, probably calculation has a lot to do with it? There comes a decisive point in most games where you have to go in for some concrete lines or else your advantage disappears.
Similarly, "practical skills" include time management, balancing your reliance on intuition vs calculation, being awake and rested for the game, balancing setting problems for the opponent with how much risk you're taking (a very individual balance), staying alert and looking for chances even in bad positions, lots of sports psychology, etc. I find Jacob Aagaard has useful things to say about sports psychology in chess, i.e. in
Excelling at Chess. I haven't read his recent
Thinking Inside the Box though. Jonathan Rowson too, but I liked
Chess for Zebras a lot better than
The Seven Deadly Chess Sins.
If you really get stuck trying to figure this out, a coach could probably help.
Edit 2: A final thought: From personal experience the difference between different levels quite often comes down to how good people are at
prophylactic thinking, including how deeply and consistently they do it at the board. Would recommend reading up on that if you haven't already. Dvoretsky had a great, classical chapter on it in
Secrets of Positional Play and now also an entire book I believe. Aagaard, Rowson and many others also discuss it. The experience of being "out-prophylactized" can involve the frustrating feeling that "I foresaw what he was going to do, but just too late to stop it without negative consequences". I notice you did alright on "Recognizing threats", "Defense" and Counterattack" on the test, but there are many levels to prophylaxis.