Is it normal that my 3 year old cannot entertain himself *at all*?!

My three year old son has to constantly be entertained. He cannot play or do anything alone. From the moment he wakes up he begs me to play with him, to the point I cannot even nurse my 12 month old without him by my feet whining “mommy play with me in my room.” He’s always been like this, even before I had his brother. My 12 month old will play with his toys for like an hour independently, but my 3 year old has never done this. He stares at toys like he doesn’t know what to do. He won’t go into his room alone or do anything independently. If he’s eating, I also have to be next to him in the same room or he screams bloody murder. I am so exhausted. I have gotten to the point where I tell him to “leave mommy alone” and he stares at me crestfallen and just whines at my feet for me to play with him. But I cannot play with him 24/7! It’s not realistic! I don’t know how to teach him to play by himself. Is this normal? What do I do?