It can easily be read as funny little books following the sagas of recuring (anti)heroes. But the light-hearted stories belie a sharp-eyed critique of society, with the most well known example probably being Vimes' Boot theory of socioeconomic unfairness.
Often, the subtility is hidden in a word or a choice of words that can easily go unnoticed, but are all small hints of the vast pluridisciplinary depth of knowledge of the author. The esoteric, historical, literary and physical sciences references (to name just them), are delightful small winks to the reader sprinkled throughout the books.
The Sword in the Stone is pretty good in this regard. Apart from that first book (which is published as a standalone book) the entire Once and Future King is too complex for a child, I think (instead it would come off as boring and obscure).
But in general almost any book a kid wants to try to read will be fine.
Also: back in the day when small towns had a single cinema screen, movies would travel around as physical media and play for a week or two. So they had to be appropriate for anyone in town else the cinema owner wouldn’t take them.
My kid loved those Fred Astaire musicals. I do too. For him they were just fun. To me, many of them were quite racy and quite explicit! But all that just went over his head.
* Island of the Blue Dolphins
* Chronicles of Prydain (Book of Three, The Black Cauldron, etc)
Chronicles of Narnia aren't Newberry winners, but are good regardless (if you don't mind the religious subtext).
+1 for other people mentioning The Hobbit and Lord of the Rings.
Our whole family has enjoyed classics like Pride and Prejudice and Dracula -- such books are called "classics" for a reason.
Modern YA fiction has some very good books as well -- we all enjoyed Hole by Louis Sachar.
Some good modern sci-fi too -- Project Hail Mary by Andy Weir was well received, as was Ender's Game.
Brandon Sanderson's stuff is very good. Whole family enjoyed The Way of Kings and the books that follow.
(For context, "whole family" is mix of genders, ages 10-15)
Jonathan Swift: Gulliver's Travels
Umberto Eco: The Name of the Rose
Bohumil Hrabal: Cutting it Short
Antal Szerb: The Pendragon Legend
A good portion of the book are philosophical discussions, which would be IMHO very boring and not understandable for small children.
The magic of novels like Svejk or Little Prince is that those extra layers are mostly implied, emergent, they're not written out explicitly and thus don't bore out the young readers.
In addition to what the other replies recommended, I read Tom Sharpe at a young age and enjoyed all of them with sometimes uncontrollable giggles.
Start with Wilt, I think. Then maybe The Throwback.
His short stories are beyond fascinating and adorable, BTW. One, for example, equates accounting to hunting and detective work.
The Stars My Destination by Alfred Bester.
Works of James Herriot.
IIRC, the name for rabbit was kebbo or something like that, so if you called out the true name for rabbit, any and all rabbits would be affected. This would then hold for petals as well?
Also, the secret to exiting the school (getting past the guardian) was pretty cool.
I disliked it as a kid for the same reasons I've loved it (and Exupéry's other aviator stories) as adult: it's abstract and impressionist.
Intruder in the Dust, the best of William Faulkner's "young adult" novels. The short story collection Knight's Gambit is also well worth a look.
The Adventures of Huckleberry Finn. My mother read it to me before I could read. I thought it was a great adventure book!
For a child, it's a slapstick comedy about Satan's retinue's visit to Soviet Moscow.
For a teen, it's a savage political satire taking down Stalinism.
For an adult, it's philosophy...