improving tremendously in your 50s - some prove

Not sure. Maybe a notorious „benefitter“ of the 400-points Elo rule.

It seems he is constantly playing very strong opposition, too. And he hardly ever loses a game.

Read this morning that one has found his mobile on a toilet...

Rausis is FIDE arbiter and trainer himself. Oh dear!

„some prove“ - here it is.

Dude goes 25 years between appearances in the world top 100? Gained 200 points in a couple of years in his fifties? Blatantly suspicious and no shock to learn he is cheating. What else does anybody think actually happened? He went from 2500 to 2700 after decades well below that level by memorizing a couple of openings or something? That is completely unrealistic.

And all this time, I thought the secret to his success was plenty of fiber in his diet.

Do big improvements (+200 points or more) in chess skill require a comprehensive review of one's games plus intensive study in the three phases (opening, middle, and ending) of the chess games of best chess players, past and present?

What good chess books do you recommend?

Improving always concerns „the full monty“. Hard work on everything over decades.

There are no short-cuts and no special points, it‘s virtually „all“. Playing complete games, training everything and analyze it completely. Practice > theory.