Summary

Closes #11215

Adds a warning to the "Return a Response Directly" docs page explaining that returning a Response with a background parameter silently overrides any BackgroundTasks added via dependency injection.

Problem

When an endpoint uses both BackgroundTasks dependency injection and returns a Response(background=BackgroundTask(...)), the injected tasks are silently dropped. This happens because fastapi/routing.py only assigns injected background tasks when response.background is None:

if raw_response.background is None:
    raw_response.background = solved_result.background_tasks

This is a common footgun with no runtime warning -- tasks simply don't execute.

Changes

• Added a //github.com/ warning block to docs/en/docs/advanced/response-directly.md explaining the interaction
• Created docs_src/response_directly/tutorial003.py with correct and incorrect patterns
• Follows existing callout conventions used in docs/en/docs/tutorial/background-tasks.md

Motivation

I use FastAPI BackgroundTasks across 5 production APIs and nearly hit this exact issue when refactoring webhook delivery to return custom Response objects. The current docs don't mention this interaction anywhere.

Test plan

• Warning uses //github.com/ warning block syntax (FastAPI convention)
• Example file follows existing tutorial naming pattern
• Example is importable Python

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