Can you dissect how the blurred background have been done while keeping foreground in focus?

TL;DR: in a word, photoshop. (in the sense of xerox, band-aid, or kleenex. Digital jiggery-pokery, whatever the actual editing software used).

This has undoubtedly been heavily processed.

1. All of the background trees have more-or-less defined edges, but absolutely no bark knot holes. Some of the lower parts of them have the color of the rough bark that aspens take on, but it is just sort of smudged into the white. Lens bokeh will not smudge details like that, and eliminate any coloration from bark knots, but leave the edges of the trees so well defined. I think some vertical blur or smudging has been applied to the background trees, and several translucent layers of mist applied over them.

2. The foreground was stacked as a separate layer from the background. None of the "mist" affects the foreground. Look at the 3rd prominent shadow from the bottom, the one that goes behind the 3 foreground trees, and looks to dead-end at the farthest left foreground tree. Why is that shadow so light gray, while the 2-3 shadows immediately in front of it are pitch black? Light doesn't work that way. Also, if you follow the shadow of the farthest left tree that isn't blurred, how does the blurred tree at the very left edge continue below/in front of the shadow?

Other people could probably go on in more detail. I'm not trying to tear this apart like moon landing conspiracy theorists. It's just that there is obvious signs of Photoshop here. It's decent art, to my eye. But the magic isn't convincing, that's all.