Construct 2/exporters/html5/favicon.ico is where you need to look. This icon is only used during preview - not sure why you'd care to change it.
The icon files in the project are used to create the icon shown in the browser tab only when you run an exported project. I guess you're not running an exported project...
See the links above. They show exported files of project and the secod link is working example with these files. It shows a gear, though I exported that as html5 and changed icons. That means favicon is not only for preview right?
If I have to change tat file everytime I want to export a game, that's kinda strange
UPD: my friends who checked the example said that they didn't see any gears. But why I see that everytime I launch it?