As a user, I can query the Task Service (or endpoint), and obtain User Tasks that contain the extension properties defined in the corresponding Process Definition.

AT:

• The Java API TaskService returns User Tasks with extension properties included.
• The Java API HistoryService returns Historic User Tasks with extension properties included.
• The Rest API Task Get & Get List (GET/POST) endpoints return User Tasks with extension properties included.
• The Rest API History Get & Get List (GET/POST) endpoints return User Tasks with extension properties included.

Original request description:

In the modeler we can set properties as extension on tasks.

The External Task endpoint now allow to expose them using a flag by (https://jira.camunda.com/browse/CAM-12080), it would be nice to have the same for Task endpoint.

In our application we use Camunda as to dictate the flow of task to completed to a certain process, we assign user on these task, but form are not in camunda, because we needed more flexibility on the frontend part. We use a backend in C# and a frontend in VueJS. We don't want to associate a URL to a task because they can change between environment and for other reason so we use a route name that is resolve in our frontend, the route name is store in extension properties of the task. So when task is active we can get the route name by inspecting the task extension properties. (we use them for other thing too). Right now, we pull the BMPN of the same version of the process attach to the task using the BPMN endpoint. We store the task extension properties per task per process-version in Dictionary (MAP) to avoid calling each time the endpoint for the same process version. If we could have a flag on the task endpoint like the one for FetchAndLock of External Task we could  remove this awkward logic.