Yeah....technically. But Disney hasn't exactly been leaning into the British angle for its entire history. Other than the British narrator, who just sounds like any kindly narrator, the whole thing is pretty Americanized. The characters don't have British dialects or make references to English things or phrases.
Disney's Pooh is as British as Disney's Snow White is German and Cinderella is French.
The Pooh books’ identity as a distinctly British creation is well known by most fans. Christopher Robin and the narrator are both played by British actors in all the *good* Pooh films. Walt Disney insisted on adding the American Gopher character, but aside from that let the director keep it Mary Poppins-level British (in tone), right down to the look of the kid’s room.
But I agree with your main point… except that, even then, I think Pooh has no more place in an American-themed woodsy land than Mr. Toad, the Aristocats, Robin Hood, the cast of Zootopia, The Great Mouse Detective, Chicken Little, The Three Caballeros, Ducktales, or many other animal IPs.
The Rescuers or Fox & the Hound… sure.
I know, it’s just a theme park and no land is 100% bound to it’s theme (or even needs to be) and I normally wouldn’t mind a below-average dark ride, but in this case… have I ever mentioned how much I loved The Country Bears and how much I dislike its joke-of a-replacement? Love the queue music loop, though.