[Docs] use `uv` in CPU installation docs (#22089)

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

docs/getting_started/installation/cpu/apple.inc.md

 # --8<-- [start:installation]
 
-vLLM has experimental support for macOS with Apple silicon. For now, users shall build from the source vLLM to natively run on macOS.
+vLLM has experimental support for macOS with Apple silicon. For now, users must build from source to natively run on macOS.
 
 Currently the CPU implementation for macOS supports FP32 and FP16 datatypes.
 
@@ -23,20 +23,20 @@ Currently the CPU implementation for macOS supports FP32 and FP16 datatypes.
 # --8<-- [end:pre-built-wheels]
 # --8<-- [start:build-wheel-from-source]
 
-After installation of XCode and the Command Line Tools, which include Apple Clang, execute the following commands to build and install vLLM from the source.
+After installation of XCode and the Command Line Tools, which include Apple Clang, execute the following commands to build and install vLLM from source.
 
 ```bash
 git clone https://github.com/vllm-project/vllm.git
 cd vllm
-pip install -r requirements/cpu.txt
-pip install -e .
+uv pip install -r requirements/cpu.txt
+uv pip install -e .
 ```
 
 !!! note
-    On macOS the `VLLM_TARGET_DEVICE` is automatically set to `cpu`, which currently is the only supported device.
+    On macOS the `VLLM_TARGET_DEVICE` is automatically set to `cpu`, which is currently the only supported device.
 
 !!! example "Troubleshooting"
-    If the build has error like the following snippet where standard C++ headers cannot be found, try to remove and reinstall your
+    If the build fails with errors like the following where standard C++ headers cannot be found, try to remove and reinstall your
     [Command Line Tools for Xcode](https://developer.apple.com/download/all/).
 
     ```text

docs/getting_started/installation/cpu/build.inc.md

-First, install recommended compiler. We recommend to use `gcc/g++ >= 12.3.0` as the default compiler to avoid potential problems. For example, on Ubuntu 22.4, you can run:
+First, install the recommended compiler. We recommend using `gcc/g++ >= 12.3.0` as the default compiler to avoid potential problems. For example, on Ubuntu 22.4, you can run:
 
 ```bash
 sudo apt-get update  -y
@@ -6,28 +6,34 @@ sudo apt-get install -y --no-install-recommends ccache git curl wget ca-certific
 sudo update-alternatives --install /usr/bin/gcc gcc /usr/bin/gcc-12 10 --slave /usr/bin/g++ g++ /usr/bin/g++-12
 ```
 
-Second, clone vLLM project:
+Second, clone the vLLM project:
 
 ```bash
 git clone https://github.com/vllm-project/vllm.git vllm_source
 cd vllm_source
 ```
 
-Third, install Python packages for vLLM CPU backend building:
+Third, install required dependencies:
 
 ```bash
-pip install --upgrade pip
-pip install -v -r requirements/cpu-build.txt --extra-index-url https://download.pytorch.org/whl/cpu
-pip install -v -r requirements/cpu.txt --extra-index-url https://download.pytorch.org/whl/cpu
+uv pip install -r requirements/cpu-build.txt --torch-backend auto
+uv pip install -r requirements/cpu.txt --torch-backend auto
 ```
 
-Finally, build and install vLLM CPU backend:
+??? console "pip"
+    ```bash
+    pip install --upgrade pip
+    pip install -v -r requirements/cpu-build.txt --extra-index-url https://download.pytorch.org/whl/cpu
+    pip install -v -r requirements/cpu.txt --extra-index-url https://download.pytorch.org/whl/cpu
+    ```
+
+Finally, build and install vLLM:
 
 ```bash
 VLLM_TARGET_DEVICE=cpu python setup.py install
 ```
 
-If you want to develop vllm, install it in editable mode instead.
+If you want to develop vLLM, install it in editable mode instead.
 
 ```bash
 VLLM_TARGET_DEVICE=cpu python setup.py develop

docs/getting_started/installation/cpu/s390x.inc.md

 # --8<-- [start:installation]
 
-vLLM has experimental support for s390x architecture on IBM Z platform. For now, users shall build from the vLLM source to natively run on IBM Z platform.
+vLLM has experimental support for s390x architecture on IBM Z platform. For now, users must build from source to natively run on IBM Z platform.
 
 Currently the CPU implementation for s390x architecture supports FP32 datatype only.
 
@@ -40,12 +40,23 @@ curl https://sh.rustup.rs -sSf | sh -s -- -y && \
     . "$HOME/.cargo/env"
 ```
 
-Execute the following commands to build and install vLLM from the source.
+Execute the following commands to build and install vLLM from source.
 
 !!! tip
-    Please build the following dependencies, `torchvision`, `pyarrow` from the source before building vLLM.
+    Please build the following dependencies, `torchvision`, `pyarrow` from source before building vLLM.
 
 ```bash
+    sed -i '/^torch/d' requirements-build.txt    # remove torch from requirements-build.txt since we use nightly builds
+    uv pip install -v \
+        --torch-backend auto \
+        -r requirements-build.txt \
+        -r requirements-cpu.txt \
+    VLLM_TARGET_DEVICE=cpu python setup.py bdist_wheel && \
+        uv pip install dist/*.whl
+```
+
+??? console "pip"
+    ```bash
         sed -i '/^torch/d' requirements-build.txt    # remove torch from requirements-build.txt since we use nightly builds
         pip install -v \
             --extra-index-url https://download.pytorch.org/whl/nightly/cpu \
@@ -53,7 +64,7 @@ Execute the following commands to build and install vLLM from the source.
             -r requirements-cpu.txt \
         VLLM_TARGET_DEVICE=cpu python setup.py bdist_wheel && \
             pip install dist/*.whl
-```
+    ```
 
 # --8<-- [end:build-wheel-from-source]
 # --8<-- [start:pre-built-images]
@@ -65,16 +76,16 @@ Execute the following commands to build and install vLLM from the source.
 docker build -f docker/Dockerfile.s390x \
     --tag vllm-cpu-env .
 
-# Launching OpenAI server
+# Launch OpenAI server
 docker run --rm \
-            --privileged=true \
-            --shm-size=4g \
+    --privileged true \
+    --shm-size 4g \
     -p 8000:8000 \
     -e VLLM_CPU_KVCACHE_SPACE=<KV cache space> \
     -e VLLM_CPU_OMP_THREADS_BIND=<CPU cores for inference> \
     vllm-cpu-env \
-            --model=meta-llama/Llama-3.2-1B-Instruct \
-            --dtype=float \
+    --model meta-llama/Llama-3.2-1B-Instruct \
+    --dtype float \
     other vLLM OpenAI server arguments
 ```