The Windows Default web browser cannot be edited or deleted from the Browser list. It is not an actual web browser. It merely refers to the web browser that Windows uses when you open an Internet shortcut on the Desktop. The browser that is started is controlled via settings in Windows configured by your web browser and is something Search Bar Pro has no control over.
Not all web browsers work are able to set themselves as the default browser in Windows. If you are having problems getting Search Bar Pro to work with your web browser, you can add it as another browser.