Currently, there is no specific setting mentioned in the provided context that allows you to disable Microsoft Edge from opening when you like a wallpaper at the login screen. This behavior seems to be a feature of Windows that is tied to how wallpapers are managed and displayed.
If you want to manage how web links open from applications like Outlook or Teams, you can configure policies to control which browser opens web links, but this does not directly address the wallpaper liking feature at the login screen.
For now, you might consider providing feedback to Microsoft regarding this feature, as user feedback is valuable for improving products. You can do this by pressing alt + shift + I in Microsoft Edge to open the feedback dialog.