[Docs] Add docs for context extension using the yarn method (#37430)

Signed-off-by: xiaoming <1259730330@qq.com>
Signed-off-by: labAxiaoming <34019940+labAxiaoming@users.noreply.github.com>
Co-authored-by: Cyrus Leung <cyrus.tl.leung@gmail.com>

docs/features/context_extension.md

+# Context Extension
+
+!!! note
+    The `--rope-scaling` parameter used in older versions of vLLM is no longer supported. Please use the `--hf-overrides` method with `rope_parameters` instead.
+This directory contains examples for extending the context length of models using vLLM.
+
+## Offline Inference Example
+
+The [`context_extension.py`](../../examples/offline_inference/context_extension) script demonstrates how to extend the context length of a Qwen model using the YARN method (rope_parameters) and run a simple chat example.
+
+### Usage
+
+```bash
+python examples/offline_inference/context_extension.py
+```
+
+## OpenAI Online Method
+
+You can also use vLLM's OpenAI-compatible API to serve models with extended context length.
+
+### Usage
+
+Run the vLLM server with the following command to extend the context length using YARN:
+
+```bash
+vllm serve Qwen/Qwen3-0.6B \
+  --hf-overrides '{"rope_parameters": {"factor": 4.0, "original_max_position_embeddings": 32768, "rope_theta": 1000000, "rope_type": "yarn"}}' \
+  --max-model-len 131072
+```
+
+### Client Example
+
+After starting the server, you can use the OpenAI Python client to interact with it:
+
+```python
+from openai import OpenAI
+
+client = OpenAI(
+    base_url="http://localhost:8000/v1",
+    api_key="token-abc123"  # Dummy API key, required by the client
+)
+
+response = client.chat.completions.create(
+    model="Qwen/Qwen3-0.6B",
+    messages=[
+        {"role": "system", "content": "You are a helpful assistant"},
+        {"role": "user", "content": "Hello"}
+    ],
+    max_tokens=128,
+    temperature=0.8,
+    top_p=0.95
+)
+
+print(response.choices[0].message.content)
+```
+
+### Key Parameters
+
+The available parameters depend on the `rope_type` you choose. For detailed information about all supported RoPE types and their specific parameters, please refer to the [Hugging Face Transformers RoPE documentation](https://huggingface.co/docs/transformers/main/en/internal/rope_utils#transformers.RopeParameters).
+
+Common parameters include:
+
+- `rope_type`: The type of RoPE implementation (e.g., "yarn", "linear", "dynamic")
+- `factor`: The factor by which to extend the context length
+- `original_max_position_embeddings`: The original maximum position embeddings of the model
+
+The following parameters are specific to vLLM:
+
+- `max_model_len`: The new maximum sequence length after extension (original * factor).
+  Used for KV cache pre‑allocation and request limit at serving time.