docs: Fix testing code examples

docs/usage/testing.rst

@@ -116,17 +116,43 @@ We would then be able to rewrite our test like so:
     .. tab-item:: Sync
         :sync: sync
 
-        .. literalinclude:: /examples/testing/test_health_check_sync.py
+        .. code-block:: python
             :caption: tests/test_health_check.py
-            :language: python
+
+            import pytest
+
+            from litestar.status_codes import HTTP_200_OK
+            from litestar.testing import TestClient
+
+            from app import app
+
+
+            def test_health_check_with_fixture(test_client: TestClient) -> None:
+                with test_client as client:
+                    response = client.get("/health-check")
+                    assert response.status_code == HTTP_200_OK
+                    assert response.text == "healthy"
 
 
     .. tab-item:: Async
         :sync: async
 
-        .. literalinclude:: /examples/testing/test_health_check_async.py
+        .. code-block:: python
             :caption: tests/test_health_check.py
-            :language: python
+
+            import pytest
+
+            from litestar.status_codes import HTTP_200_OK
+            from litestar.testing import AsyncTestClient
+
+            from app import app
+
+
+            async def test_health_check_with_fixture(test_client: AsyncTestClient) -> None:
+                async with test_client as client:
+                    response = await client.get("/health-check")
+                    assert response.status_code == HTTP_200_OK
+                    assert response.text == "healthy"
 
 
 Using sessions
@@ -141,7 +167,7 @@ across requests, then you might want to inject or inspect session data outside a
 
 .. attention::
 
-    - The Session Middleware must be enabled in Litestar app provided to the TestClient to use sessions.
+    - The session middleware must be enabled in the Litestar app provided to the :class:`TestClient <.testing.TestClient>` to use sessions.
     - If you are using the
       :class:`ClientSideSessionBackend <litestar.middleware.session.client_side.ClientSideSessionBackend>` you need to
       install the ``cryptography`` package. You can do so by installing ``litestar``:
@@ -162,7 +188,7 @@ across requests, then you might want to inject or inspect session data outside a
 
                 pipx install litestar[cryptography]
 
-        .. tab-item:: pdm
+        .. tab-item:: PDM
 
             .. code-block:: bash
                 :caption: Using `PDM <https://pdm.fming.dev/>`_
@@ -229,7 +255,7 @@ an instance of Litestar and then a test client using it. There are multiple use
 generic logic that is decoupled from a specific Litestar app, or when you want to test endpoints in isolation.
 
 You can pass to this helper all the kwargs accepted by
-the litestar constructor, with the ``route_handlers`` kwarg being **required**. Yet unlike the Litestar app, which
+the Litestar constructor, with the ``route_handlers`` kwarg being **required**. Yet unlike the Litestar app, which
 expects ``route_handlers`` to be a list, here you can also pass individual values.
 
 For example, you can do this:
@@ -341,7 +367,7 @@ Using polyfactory
 ------------------------
 
 `Polyfactory <https://github.com/litestar-org/polyfactory>`__ offers an easy
-and powerful way to generate mock data from pydantic models and dataclasses.
+and powerful way to generate mock data from Pydantic models and dataclasses.
 
 Let's say we have an API that talks to an external service and retrieves some data:
 
@@ -401,7 +427,7 @@ We could test the ``/item`` route like so:
 
 While we can define the test data manually, as is done in the above, this can be quite cumbersome. That's
 where `polyfactory <https://github.com/litestar-org/polyfactory>`_ library comes in. It generates mock data for
-pydantic models and dataclasses based on type annotations. With it, we could rewrite the above example like so:
+Pydantic models and dataclasses based on type annotations. With it, we could rewrite the above example like so:
 
 
 .. code-block:: python