My DS is 3, about to be 4, and tonight I've had to tell him to many many many many times to sit down and face his food, hold his taco over his plate, don't jump in the kitchen, stop with the feet (kicking them about, digging them into things) and no more mouth noises please. He's not a climber but he will just roll all over the furniture.
He's also super clever, very kind and gentle though full on. He is my world but when he's alsleep, we breathe a sigh of relief.
I don't get him till 5 and our fee covers 8-6 so if he needs to be there longer because I'm working, then he is. He's only ever been the last kid twice and I've felt bad then.
As for cartoons, he will get a choice of two (eg Peppa or Bluey) and often one of those will be a 90s cartoon. They are calmer. We are working through:
Rupert, Arthur, Blues Clues, Sesame Street, Magic School Bus, Little Bear, Daniel Tiger, Mr Rogers etc
Anything that makes bad behaviour we have stopped (eg Blippi made him feral and walk silly constantly)
We read a lot of books and he can read them too. This does lead to a lot of questions and interruptions. We are trying to say no questions until the page is done at least.
I don't let him the tablet except for a few educational apps Duolingo ABC is really good. And he does one that names bones in the body. No tablet after a certain time. Considering a Tonee box for next birthday.
Maybe some of those will be helpful if you haven't tried. That said, my sweet clever boy is still wild, tests my patience and drives me mad every day. Three is hard.