@Holomew Thanks for reaching out. Can you please confirm if you are using service bus trigger and iterating the output inside for each loop?
If this is the scenario then you can use the dynamic output Content on the current item and the result should only return your actual message content.
Logic app does support different JSON & XML Manipulation function which you can leverage to perform different operations. In your case if you want to only get the contentData object then you can leverage the parse json action which will create the user-friendly fields or tokens for those properties by using the Parse JSON action. Now you can leverage these tokens in any of the next actions in your workflow to get the value of contentData
token created by Parse Json action.
Logic app already provide the dynamic objects so you can always leverage the dynamic object return by any action. In case if your requirement is not fulfilled using dynamic output then you can always leverage other actions/functions for your desired output.