Search notes:

Registry: HKEY_CURRENT_USER\Software\Microsoft\Office\X.Y\Outlook\Preferences

NewMailDesktopAlerts

The following PowerShell script sets the value of NewMailDesktopAlerts to 0 which stops the annoying desktop alert when new mails arrive: 
new-itemProperty -path HKCU:\Software\Microsoft\Office\16.0\Outlook\Preferences -name 'NewMailDesktopAlerts' -value 0 -force
Github repository about-Windows-Registry, path: /HKEY_CURRENT_USER/Software/Microsoft/Office/application_version/Outlook/Preferences/NewMailDesktopAlerts.ps1

Index