[Doc] update Contributing page's testing section (#18272)

Signed-off-by: David Xia <david@davidxia.com>

docs/contributing/README.md

@@ -26,6 +26,8 @@ See <gh-file:LICENSE>.
 
 ## Developing
 
+--8<-- "docs/getting_started/installation/python_env_setup.inc.md"
+
 Depending on the kind of development you'd like to do (e.g. Python, CUDA), you can choose to build vLLM with or without compilation.
 Check out the [building from source][build-from-source] documentation for details.
 
@@ -42,7 +44,7 @@ For an optimized workflow when iterating on C++/CUDA kernels, see the [Increment
 Install MkDocs along with the [plugins](https://github.com/vllm-project/vllm/blob/main/mkdocs.yaml) used in the vLLM documentation, as well as required dependencies:
 
 ```bash
-pip install -r requirements/docs.txt
+uv pip install -r requirements/docs.txt
 ```
 
 !!! note
@@ -98,13 +100,14 @@ For additional features and advanced configurations, refer to the official [MkDo
 ??? console "Commands"
 
     ```bash
-    pip install -r requirements/common.txt -r requirements/dev.txt
+    # These commands are only for Nvidia CUDA platforms.
+    uv pip install -r requirements/common.txt -r requirements/dev.txt --torch-backend=auto
 
     # Linting, formatting and static type checking
-    pre-commit install --hook-type pre-commit --hook-type commit-msg
+    pre-commit install
 
     # You can manually run pre-commit with
-    pre-commit run --all-files
+    pre-commit run --all-files --show-diff-on-failure
 
     # To manually run something from CI that does not run
     # locally by default, you can run:
@@ -122,6 +125,10 @@ For additional features and advanced configurations, refer to the official [MkDo
 
     Therefore, we recommend developing with Python 3.12 to minimise the chance of your local environment clashing with our CI environment.
 
+!!! note "Install python3-dev if Python.h is missing"
+    If any of the above commands fails with `Python.h: No such file or directory`, install
+    `python3-dev` with `sudo apt install python3-dev`.
+
 !!! note
     Currently, the repository is not fully checked by `mypy`.