Do you think zombies are aware of other zombies?

I’m using the classic, slow moving Romero zombies for this question.
I’m of the mind that a zombie is not aware of any other zombies around him, at least, not anymore than he might be aware of an inanimate obstacle, like a door or a car.
I base this on something I frequently see in older movies. Say a zombie is munching out on a human hand, and another zombie without anything to eat walks by, he’ll go for the hand that the first zombie is eating. He’ll grab it, yank on it and try to obtain it for himself. It’s like he only registers the food, and not the being holding it. A zombie will never seem to attack another zombie and then get the food. Hostility only occurs when the other zombie wants to protect his food, and even then, THAT zombie doesn’t seem to register the undead thief, he just yanks and tries to protect his food.
A funny exception is that weird zombie in Night of the Living Dead who’s slowly banging a foot on the floor over and over, until another zombie walks by and grabs it. The first zombie doesn’t even do anything, he just keeps banging his hand on the ground. However, zombies have cycles, and are much less aggressive when they’ve just fed, so I assume that this one zombie had its share for the moment.

They also sway around, bump into each other and act like nobody’s there, although this is easily credited to their physical disposition. But still.

Now, I realize that the exceptions are plenty. All the zombies in the end of Dawn of the Dead following zombified Flyboy as he leads them to Fran and Peter. (although to me, that is complete anomaly)
But movies have to include stuff like that, if they wanna be a good movie. Zombies are a simple concept and you can do a lot of stuff with them, but it does have its limits that cannot be ignored when it comes to usual movie plot twists and surprises.

Or the fact that zombies can learn to primitively interact with their surroundings, like opening doors or trying to drive a car. But to me, this remains a completely scientific remnant of their former selves, which has nothing to do with how sentient they are, or are not. And aye, I’m quite aware of Bub from Day of the Dead.

So which do you think it is? Are zombies aware of other zombies, or anything else for that matter, other than what their instinct interprets as food?

Perhaps they’re unaware, but may be conditioned to learn, or conditioned to be aware, like a lot of movies show?

I’m highly convinced that a zombie is not aware of another zombie. However, I love to learn about zombies, and would love to hear what the collective has to say. Humor, as always, is welcome.