How to apply Color Managenment to an image?

I’m struggling with exporting image. After rendering I’ve done compositing including Color Management and have exported image as 16 bit PNG, but then I’ve noticed that Color Management ajustments are not presented in image. So I tried to export image as 8/16/32 bit images and different formats, but it changed nothing.
Viewport:


Output image:

Color Managenent settings:

I mean if Color Managenent is not affecting final image, what’s the point of using it, Filmic and other things?

“Save As Render” applies the display transform set from Color Management tab.

saveasrender

Thanks, it worked! It should be enabled by default, but in my case it was somehow disabled in all projects