However, the new native app still just displays the Copilot website ... It also places a Copilot icon in the System Tray for some reason. Of course, this new Copilot app is in preview, so ...

we now have the option to pick any image file as a custom icon when adding a web app to the Dock from Safari. As on iOS and iPadOS, macOS will even fit this image into a rounded square after the fact ...