Impossible depth of field

This is a keel-billed toucan I photographed in Costa Rica with a Canon 500mm f/4 telephoto. It was attracted to a feeder with several kinds of fruit set up by the lodge I was using. Obviously, with a long lens the background would be out of focus. I like the original image a lot, but in this instance I replaced the non-descript foliage background with a sharp tropical landscape. Both images were taken in the same diffused lighting -- that’s important for realism -- and notice the angle as well. I was shooting upward toward the bird, and the same upward angle was used to capture the trees and the sky. I waited for the bird to turn its head so that incredible beak was parallel with the plane of the digital sensor so I'd have complete depth of field. To make a precise selection around the toucan, the branch, and the small plant growing in the branch, I used Topaz Mask AI. My settings for the image of the bird were 1/125, f/9,1000 ISO, and I used a tripod.