Does your rating express the quality of your play regardless of time control? For instance if I analyze a game played in blitz, move by move, between two 2600s, should I expect the moves to be of the same quality as the moves between two 2600s in classical? Or would worse play in blitz be enough to achieve a 2600 rating, given that every player is playing worse moves due to time pressure?

So if someone who's, for instance, 1600 in classical, 1400 in rapid, and 1200 in blitz, does this mean that they are especially reliant in longer time controls and have a pronounced difficulty in performing under time pressure (more so than other people), or is this drop-off in rating expected, because everyone plays worse under time pressure?
The way ratings are mathematically defined, they don't express the absolute strength of players, but only the strength of players in a pool relative to each other. So there is no meaning in trying to compare blitz rating and standard rating, the way you are trying to suggest.

For the same reason you cannot compare computer ratings with human ratings, because they are calculated from different pools: computers playing only against computers vs humans playing only against humans. 

Also for the same reason you cannot really compare ratings on different websites or online ratings with FIDE ratings.



That being said, most of the good players (above say 2600 in standard) are also decent Blitz players and would have a comparable blitz rating. 

Still, speaking of absolute strengths, their blitz games would (on average) be worse quality than their standard games.

Giving a concrete example: Ding Liren and Hikaru Nakamura both have blitz and standard ratings in the 2800. So they are equal in strength in blitz (compared to each other) and in standard, but that is because they are equally worse in blitz....