It seems to me... that Construct doesn't support transparent .ico files. It makes white background anyway...
If you use the picture editor to make your icon, or open a png or bmp file in the picture editor, then it supports transparency.
I've created transparent icons for my games like this.
Use PNG.
Develop games in your browser. Powerful, performant & highly capable.
Minor
The problem is... that I've already made an .ico file...
I did so to! But anyway after exporting to EXE there is a white background
Use the colour 255,0,255 to fill the area you want to be transparent. This is the "Magic Pink" colour that Construct and other programs use as transparent.
Hate that pink.... It makes my eye bleed if whole background is that colour etc.... something more "peaceful" colour would be better