I’m not an authority on this but I believe that objectively a character WILL look like “that” but when viewed subjectively they look like “this”. So, in short, to answer your question: yes, but not really. I hope this helps.
It depends on the author! Authors create symbolic universes and they get to choose the rules of those universes. You can read Robert McKee’s work for more on this.
You occasionally get situations when the animators switch the art style every now and then, but the characters still exist in the same universe, so I wonder if the characters wonder why everything looks slightly different.
In Star Trek SNW's crossover episode with Lower Decks (cartoon), Boimler's first comment when he meets the crew from SNW is that they look "very realistic"
I remember something with a cartoon character commenting on how live-action people look kind of disturbing and surreal. They noticed the difference, and it didn’t sit well with them. Their own uncanny valley.
And the first thing he did in the 3D world was go to an erotic bakery. I always thought it was a dumb throwaway joke but after thinking about it, that would be a fun first experience in the 3D world
The other characters are quite perplexed about the idea of 3D, too, not just the stupid Homer. A scientist gives a brief lecture, similar to how scientists IRL introduce 4D.
Anyway, that answers the good old question "Is the gruesome cartoon Itchy & Scratchy photorealistic from the Simpson's POV?"
Photorealistic: yes. However, it could be debatable whether it's gruesome. We see situations that characters survive with short term damage but no long term consequences (example: Homer skating into the canyon). So while it would be gruesome to us, it's probably closer to slapstick to them.
Final Crisis had some of this with Thought Robot superman. Iirc they included 3D glasses so you could see Superman reach out to you in our realm one he gained concession of us. Check out some other Grant Morrison works for trippy meta fiction (pls read Animal Man)
Most cartoons I assume they just see the world as it is in the cartoon. However SpongeBob SquarePants sees it the way it looks when they do those live action segments.
Ren & Stimpy see it as a cartoon, but they see it in the style of those super gross closeup shots. "It's hiiiiideous, Stimpy!" "I'm scared, Ren!"
In Chip and Dale 2022, they explicitly refer to the "upgrade" to 3D rendering from the old painted style (like plastic surgery to them), so I assume they are fully aware of their art style.
There 2D is like our 4D. The same way we can't see 4D, they see 2D as normal and 3D is unachievable to them as for us 4D. Same with the style. They see themselves at the same style as what is normal to them.
Some times it's part of the plot, like in comics such as Gwenpool and 8-Bit Theater. But usually, from what I notice, how a character perceives the world around is not explained.