Try this. It should force Edge to reload the various search engine options.
Close Microsoft Edge.
Type cmd into search then right click on Command Prompt and run as administrator.
Copy and paste in the following code then press enter:
taskkill /im msedge.exe /f & timeout /t 3 & del "%localappdata%\Microsoft\Edge\User Data\Default\Web Data" /f
This terminates any running instance of msedge, waits three seconds for the processes to close, then deletes the Web Data file.
When you next start Edge, the default Web Data file be regenerated and you should now be able to choose Google in the address bar search options.