Footy
I did a few things, cant quite remember the sequence, but i used the burn shadow tool around the head only, using the soft edge option at about 7 or 8% till i thought it lessened the misty look. also added a touch of contrast - but only mildly
Then, and this wasnt necessary to be honest because you had already done a fine job, but increase the view to 400% and denoise the background only using the blur tool, not the denoise tool, at 100% ( its quickest at 100% but depends on whats being done )
This gives an ultra smooth background - i did no denoise on the bird at all. Then selective smart sharpen
This took 10 x longer to type than it did to do but it looks ok, IMO
PS dont know how i managed to post 2 photos so i've just removed one