Add missing `Content-Type` headers in public api

Is your improvement proposal related to a problem? Please describe.

Currently, only some responses from the public API have a Content-Type header set. This can lead to issues when the requester expects a specific content type and it is not provided.

Describe the solution you'd like

Add Content-Type headers to all responses from the public API, ensuring that they are set to the appropriate type based on the content being returned (e.g., application/json for JSON responses).

Describe alternatives you've considered

No response

Additional context

• A good starting point would be the public API router
• Please follow our contribution guide