With TomEE, the Tomcat manager has multiple aspects to be careful about:
Your browser by default accesses the HTML-based manager whereas Codehaus Cargo needs to use the text-based manager. As a result, if you want to set the RemotePropertySet.URI manually, please make sure you set the URL for the text-based manager, for example http://production27:8080/manager/text
The text-based manager requires to be accessed by a user with the manager-script role; and by default no user has that role. As a result, please make sure you modify your tomcat-users.xml file to give that role to a user.
You can read more in the Tomcat documentation: https://tomcat.apache.org/tomcat-9.0-doc/manager-howto.html