docs: add OpenAPI examples for analysis endpoints

[Neelr1912]

Description

This PR adds OpenAPI request and response examples for the analysis endpoints to improve the Swagger UI experience and make it easier for users to test APIs using the "Try it out" feature.

Changes Made

• Added request examples for:

  • /explanation/
  • /debugging/
  • /suggestions/
  • /analyze/

• Added response examples using Pydantic schema metadata.

• Added FastAPI Body(..., examples=...) support for request payloads.

• Ensured examples are included in the generated OpenAPI schema.

• Added tests to validate that request and response examples are present in /openapi.json.

Related Issue

Fixes #205

Type of Change

• Documentation update
• Test addition

Testing

• Verified OpenAPI examples appear in Swagger UI (/docs).
• Added automated tests for OpenAPI examples.
• Confirmed no endpoint behavior or business logic was changed.

Notes

Any remaining failing tests are pre-existing repository issues and are unrelated to this PR.

[Neelr1912]

Implemented OpenAPI request and response examples for:

/explanation/
/debugging/
/suggestions/
/analyze/

Also added tests to verify examples are present in the generated OpenAPI schema.

Fixes #205.