test: add tests for Request, BackgroundTasks, and new Response instance

- Add test for dependency returning different Response instance (JSONResponse)
- Add test for Request type in dependency chain
- Add test for BackgroundTasks with Depends annotation
- Update module docstring to reflect broader scope (all special types)

tests/test_response_dependency.py

@@ -1,8 +1,13 @@
-"""Test using Response type hint as dependency annotation."""
+"""Test using special types (Response, Request, BackgroundTasks) as dependency annotations.
+
+These tests verify that special FastAPI types can be used with Depends() annotations
+and that the dependency injection system properly handles them.
+"""
 
 from typing import Annotated
 
-from fastapi import Depends, FastAPI, Response
+from fastapi import BackgroundTasks, Depends, FastAPI, Request, Response
+from fastapi.responses import JSONResponse
 from fastapi.testclient import TestClient
 
 
@@ -87,3 +92,82 @@ def test_response_dependency_chain():
     assert resp.status_code == 200
     assert resp.headers.get("X-First") == "1"
     assert resp.headers.get("X-Second") == "2"
+
+
+def test_response_dependency_returns_different_response_instance():
+    """Dependency that returns a different Response instance should work.
+    
+    When a dependency returns a new Response object (e.g., JSONResponse) instead
+    of modifying the injected one, the returned response should be used and any
+    modifications to it in the endpoint should be preserved.
+    """
+    app = FastAPI()
+
+    def default_response() -> Response:
+        response = JSONResponse(content={"status": "ok"})
+        response.headers["X-Custom"] = "initial"
+        return response
+
+    @app.get("/")
+    def endpoint(response: Annotated[Response, Depends(default_response)]):
+        response.headers["X-Custom"] = "modified"
+        return response
+
+    client = TestClient(app)
+    resp = client.get("/")
+
+    assert resp.status_code == 200
+    assert resp.json() == {"status": "ok"}
+    assert resp.headers.get("X-Custom") == "modified"
+
+
+# Tests for Request type hint with Depends
+def test_request_with_depends_annotated():
+    """Request type hint should work in dependency chain."""
+    app = FastAPI()
+
+    def extract_request_info(request: Request) -> dict:
+        return {
+            "path": request.url.path,
+            "user_agent": request.headers.get("user-agent", "unknown"),
+        }
+
+    @app.get("/")
+    def endpoint(
+        info: Annotated[dict, Depends(extract_request_info)],
+    ):
+        return info
+
+    client = TestClient(app)
+    resp = client.get("/", headers={"user-agent": "test-agent"})
+
+    assert resp.status_code == 200
+    assert resp.json() == {"path": "/", "user_agent": "test-agent"}
+
+
+# Tests for BackgroundTasks type hint with Depends
+def test_background_tasks_with_depends_annotated():
+    """BackgroundTasks type hint should work with Annotated[BackgroundTasks, Depends(...)]."""
+    app = FastAPI()
+    task_results = []
+
+    def background_task(message: str):
+        task_results.append(message)
+
+    def add_background_task(background_tasks: BackgroundTasks) -> BackgroundTasks:
+        background_tasks.add_task(background_task, "from dependency")
+        return background_tasks
+
+    @app.get("/")
+    def endpoint(
+        background_tasks: Annotated[BackgroundTasks, Depends(add_background_task)],
+    ):
+        background_tasks.add_task(background_task, "from endpoint")
+        return {"status": "ok"}
+
+    client = TestClient(app)
+    resp = client.get("/")
+
+    assert resp.status_code == 200
+    assert "from dependency" in task_results
+    assert "from endpoint" in task_results