Creating your own Google App is not mandatory to use the Google Analytics and Search Console integration, indeed if you don't provide your specific credentials in JSitemap PRO configuration the default access codes will be used, that are already setup to work without any additional operation.
If you decide to create your own application you must be advised that Google has recently introduced a new system to increase security and privacy of user data, as a result you may need to request a verification to Google in order to use your application without any warning in the consent screen shown during the initial login. When you use credentials of your newly created application, the consent screen may report a warning message saying 'This app isn't verified' so that an explicit grant must be given by the user clicking on 'Go to …. appname....(unsafe)'
This consent screen appears because Google requires to verify your application before granting access to your Google Analytics data via the API integration. If you are logging in with the same account used to create the application, this screen may not be shown at all, but if you are using a different account you may be prompted with this warning about the authenticity until the app has been verified by Google.
To remove this warning in the consent screen for everyone using your Google Application, you have to submit a 'Request for verification' to the Google team using the button at the bottom of the Oauth consent screen. Once the process is completed and your app has been verified by the Google team, the consent screen will no longer include any warning.
For more informations about the verification process refer to the official Google documentation: https://support.google.com/cloud/answer/7454865
My Google Application shows 'This app isn't verified', why?