Like most elements of Superman, this depends on the version you are speaking of [Golden Age, Silver Age, Bronze Age, and Modern Age; further to that, we have Post-Crisis, New 52 and Rebirth.] Various media would portray Kryptonians extent to the knowledge as anywhere from Common place to theoretical. I'll try to find some initial examples, then modify it later when I have more time. To save time, we can broadly categorize these into Pre-Crisis and Post-Crisis examples.
Roughly from Superman's origin in 1938 to the early 50s, writers were still working out the details and extent of his abilities; this is partially why in many of hose stories you'd see him develop some odd new power "on the fly", the other being that it was comics "Golden Age" when stories were more light-hearted and heavily influenced by the George Orwell sci-fi aesthetic of the time. It is generally given that Kryptonians at this time more or less knew they were a "planet of highly evolved Supermen!" This could be seen in the recreation of superman's Golden Age Origin story, seen here....
As wasn't uncommon at the time, the Kryptonians seemed to have some limited abilities, even on their own planet. Jor-El at least knew that on a gravitationally lighter world, those abilities would be even further increased. Gravity however, and a more evolved structure, were the the very basis of these fantastic feats they pulled; sunlight seemed to have little to do with it, in story.
Later, in the 40s and 50s as his powers began to grow, a new explanation was needed; Gravity-based abilities would have him jumping far and extra strong, yes, but it wouldn't account for super senses, X-Ray vision or ice breath. So they changed it to the yellow rays of the sun giving him the majority of his abilities, and adding to his gravity and evolution based aspects, making him even stronger. This can be seen even in a 1960s comic, here, where Superman obviously new the effects it would have:
Here, from a mid 70s comic, is an example of Kryptonian scientists of indistinct era knowing the effects Earth's environment would have on them:
Now to be fair, these are all Pre-Crisis examples. I was looking for one other that spoke to how scientists on Krypton in the George Reeves Adventures of Superman show both knew that they were "superior" to other men naturally, and that "earth's atmosphere" would enhance these abilities. Unfortunately, that web comic, Panic in the Sky, seems to have been removed. So moving on to 1986's Jon Byrne reboot---- the definitive marker for Post-Crisis Superman, which more or less informs the modern era---- we have an example of Jor-El, from issue 1 of Man of Steel, showing full knowledge of what the yellow sun would do to his child.
This more or less is shown as canonical; most Post-Crisis versions, from the DCAU Superman:TAS to Smallville to the Man of Steel movie all show Jor-El speaking on the differences in the planets and what affect that will have on Kal-El's body. Here's a scan from the 2010 comic Secret Origin which shows a recording of Jor-El explaining this to the boy in his early teens.
It was a major plot point in the 9th season of Smallville; when a number of Kryptonian "Replicant" clones are released from a Kandorian orb, they are initially without there powers. A series of flashbacks explain how their powers were nullified; they were mostly soldiers, lead by Major Zod. Zod recalls to his troops how twenty years before the destruction of Krypton, the Ruling Council took their blood shortly before the destruction of Kandor, which is what was used to clone each of them on Earth. Just as Clark realizes that the clone of his father is on Earth while investigating a Kandorian landing in the desert, Jor-El arrives at the Kent Farm. Again, Jor is a scientist, so his knowledge would naturally be greater than others, but it is implied at least that this was commonly know. You can see a small clip of it here:
In the flashbacks shown, it is made explicitly clear that when the council tasked him with creating the Orb, Jor-El forewarned the council that releasing Kryptonians on earth would empower them, putting the humans at risk of subjugation. To combat this, Jor-El treated the orb with Blue Kryptonite [which, in this world, nullifies all Kryptonian powers under a yellow sun without killing them]. When his soldiers awoke, they outright asked Zod why they didn't have their abilities, and most of the season is built around their attempts to harness the sun and whatever technology they can to gain those abilities.
A final example would come from 2004's Superman: Birthright in which Jor-el, again, alludes to the effects a yellow sun would have on a Kryptonian cellular structure. Again, while him being a scientist may give Jor-el more insight,it is not implicitly stated this was the case.
So while possibly not super prevalent, I think it's fairly common knowledge amongst the Kryptonian people that they are more advanced than other humanoid races. I think the extent of their powers under a yellow sun is something only those who are in the fields of science, development, space travel or other scholarly arts may be something they have a clear idea of.