I trying to add filter to entire stage:

suspend fun main() = Korge(...) {
  this.filter = BlurFilter()
  this.invalidate()
  ...

but after that screen is black. Is it possible to add custom filter to the Stage, or another Container ?

It should be possible. At least used to work. Have you tried on JS and JVM to see if it is a bug in only one target or doesn't work consistently on all the targets?

I change filter and it works good.

filter = ColorMatrixFilter(ColorMatrixFilter.GRAYSCALE_MATRIX)

Maybe problem with BlurFilter()