Does cats know they are cute? Not likely. Cats cannot understand their appearance, nor can they understand the concept of cuteness. Although they may be happy with their appearance, they don't know what "cute" means.
Cats don't know they are cute. Cats rarely have self-awareness, and there are no criteria for judging beauty and ugliness in the population. The word cute was invented by humans. Cats do not understand human aesthetic standards, nor do they understand the meaning of the word invented by humans.
As pets, humans will have their own aesthetic standards and choose their favorite cats to keep. But for a cat, it doesn't know that it was chosen because of its appearance, nor how cute it is.