Fortunately, you can disable the desktop-click-search behavior in Bing Wallpaper’s settings—look for the one labeled “Desktop ...
As an alternative in Windows 11, you could always switch on Windows Spotlight (in Settings > Personalization > Background, in the 'Personalize your background' dropdown menu) to get your fill of ...
You can change your web browser's search engine through the browser's settings on your computer or the app or system settings on your phone.