Oh, cats definitely know you can open the door for them. When I feed our four cats, one of them (Inky) usually joins me in the cat bathroom to provide supervision services. Of course, this process must be done behind closed doors, otherwise there tends to be too much interference from some of the other cats.
Once he’s satisfied that everything is proceeding according to his plan, he looks at the door. And if I don’t open it immediately, he looks at me to try to figure out why I’m not already opening the door for him.
Every time.
He’s also the engineer who figured out how to open doors on his own, just by reaching up his longcat body, wrapping his forepaws around the door handle, and pulling. So, we had to childproof all the door handles in the house. Which is why he now has to wait for me to open the door for him.
His sister Mimi is also super smart, but she is too FOMO and doesn’t have quite the same methodical engineering mindset that Inky does.