Graph Builder and BandMaths, include input bands in output?

When I simply run BandMath from Raster -> Band Maths on a single image, the result gets added to the input image as another band.

I want this same behaviour when adding BandMaths in a graph. But what I get as an output is a product with only the results from the BandMaths operation.

Is there any way to include all of the input bands in the Graph output?

You can use the Merge operator as a second node. In this node, you can merge the source with the output of the BandMaths operator.

Is there any way to save generated band by BandMath into the original product using Graph Builder?

No, this is not possible. GPF always creates new products.