Some schools have broken up; it will be busy. Another time (or for anyone reading in the future), mid week early May is lovely. Feeling lonely at Legoland is definitely a good thing.
I remember one time where the shortest queue was for the toilets, and that was half an hour... gave up and went home.
If it's a one off, I'd buy a meal there, but take a few snacks. if you get a refillable flask on the way in then you can keep getting it refilled with cold drink. As a mean mum, I used to have one between us. Made it quite a cheap drink!
There's plenty of options, for food. All children type pizza/chicken nuggets etc.
I'd advise snacking through to lunch time, then buy something like chips. Then have an ice cream early afternoon. Then go to the all you can eat pizza. When I used to go it was half price for children after 3pm. Don't know if they still do that.
By mid afternoon you'll be thankful to have an hour sitting inside in peace and it shouldn't be too crowded then.
Start with the submarine ride down at the far end. Then with a 4yo I'd go for ones which get a lot of people on each ride. So the carousel, swings, fairy tale boats, hot air balloons, that sort of ones.
I would either go to the water area straight after the submarine or at the end of the day because the queue will almost certainly be dreadful. I think I'd be tempted to save it for the end when they're hot and bothered, but the beginning would work well too.
Taking something to spray them with water is a good idea in this heat. There were water fountains (assuming covid hasn't had them removed) so you can refill that. I have a bit of a story on the water fountains. They initially set them all up (concreted into the ground etc) so you had to use your left hand to press the button to get it to work. DD hasn't got a left hand. So I wrote to them and asked them if they could change one round so she could operate one with her right hand. Got a kind of non-answer back, but the next season when we went every single water fountain had been turned so you could operate it with either hand.
I would consider hiring one of the buggies. Then your 4yo will sit in in (and there is a roof so out of the sun) and not get as tired and hot; you have a place to put bags and generally it's easier on tempers, especially at the end of the day. You used to be able to abandon them at the bottom of the hill before going on the hill train too, which meant you didn't have to drag it back up again.
Have fun!