I feel like I can't understand how to correctly convert from ICO to PNG/GIF, preserving the transparency.
I hope that ICO supports transparency, as some of the topics from here and here give different view on the problem.
So as input I've got ICO file, which I would like to convert to GIF or PNG with preserving the transparency. First what I've noticed, is that the small images on tab do not display the transparency correctly:

The image is also shown like that when I do the export. I tried to set different colors with "Set transparency" with no positive result.
How should I do this operation in right way?
The original file is called favicon.ico in test.zip, the resulting conversion to PNG is favicon_actual.png, while I would expect something like favicon_expected.png.
XnView 1.98.2.