INCIDENT state is not returned in Public API

[engineering-issue-sync-app]

Describe the bug

When requesting process instance in incident state from Public API, the ACTIVE state is returned instead.

To Reproduce

Steps to reproduce the behavior:

1. Deploy process, start an instance and produce an incident
2. Request instance data from public API, e.g. GET /v1/process-instances/2251799814030697
3. Check the state field.

Current behavior

State is ACTIVE.

Expected behavior

State must INCIDENT.
State is unchanged, it remains as before. But in addition, the incident field is returned, of type boolean. Same as for flownode-instances API.

Environment

• Operate Version: 8.2.5

Additional context

• Forum post: https://forum.camunda.io/t/different-states-of-api-and-v1-operate-apis/45410
• Slack discussion: https://camunda.slack.com/archives/C9B5270DA/p1685643348666819
• The problem is that in Elastic we store two fields state=ACTIVE; incident=true , we changed this combination to state=INCIDENT for frontend in internal API. But we forgot to make it for Public API.
• It would be also nice to document possible state values, or to change the field type to enumeration (be careful with backward compatibility)

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Acceptance Criteria

Definition of Ready - Checklist

• The bug has been reproduced by the assignee in the environment compatible with the provided one; otherwise, the issue is closed with a comment
• The issue has a meaningful title, description, and testable acceptance criteria
• The issue has been labeled with an appropriate Bug-area label
• Necessary screenshots, screen recordings, or files are attached to the bug report

For UI changes required to solve the bug:

• Design input has been collected by the assignee

👉 Handover Dev to QA

• Changed components:

• Side effects on other components:

• Handy resources:
  BPMN/DMN models, plugins, scripts, REST API endpoints + example payload, etc :

• Example projects:

• Commands needed to test; Versions to validate:

• Docker file : in case that it needed to be tested via docker share the version contain the fixed along with version of other services .

• Release version ( in which version this fixed/feature will be released):

📗 Link to the test case

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