How useful is Chess960...

...for improving at standard chess?

The openings are completely different, but endgames tend to be very similar and the middlegames usually feature the same tactics and strategies as in standard chess. The best Chess 960 players in the world are also Grandmasters at standard chess.

How does playing chess 960 game rate for standard chess improvement against more traditional ways to study chess (e.g. learning openings, doing puzzles, studying endgames etc)?

Idk I don't even play it.

Fischer Random (960 chess) isn't really much different than standard chess; if you look at a 960 game after move 10, it usually looks like a position which might reasonably happen in a real game and almost certainly by move 20, you couldn't even tell this was a variant.

Basically, it eliminates opening theory, but the opening principles are still the same and just as important. In the opening, you mostly spend time developing pieces, controlling the center and getting castled. There really isn't much difference.

However, most chess.com games of this variant are blitz time control, so the advice against blitz chess (or for it) regarding improvement are more relevant than it being a variant:

https://www.chess.com/article/view/is-speed-chess-good-for-you

Isn't the point in Fischer Random Chess (960) and why Bobby Fischer created it was to avoid heavy Opening Theory making it an even field for players to compete with one another testing only one another's chess skills (Tactics and Endgame) and not their memory of Chess Theory.