OK, you have a very good photograph and captured some excellent action. Why focus the discussion on noise?
In film we have grain. The faster the film, the more apparent the grain. It's part of photography. The unfortunate aspect of digital is that the electrical engineering term 'noise' was used. There's nothing wrong with noise/grain. It's part of the image. So there is no need to "correct" it.
A dark overcast day. Sony 7AR4 set to 1/2000, 200mm F5.6 (Sony 200-600) auto iso @ 12800.
Timing is everything and timing was just about perfect for this confrontation between a downy and sparrow.
The noise unavoidable but can it be corrected. I’ve tried Photoshop and Topaz denoise with almost no effect. This OOC image just won’t correct. Any ideas how I can smooth out that background? BTW, shot was through a glass door.
Image, uncorrected, resized, jpg from raw file.