[Doc] Unify structured outputs examples (#18196)

Signed-off-by: Aaron Pham <contact@aarnphm.xyz>

examples/online_serving/structured_outputs/README.md

@@ -0,0 +1,54 @@
+# Structured Outputs
+
+This script demonstrates various structured output capabilities of vLLM's OpenAI-compatible server.
+It can run individual constraint type or all of them.
+It supports both streaming responses and concurrent non-streaming requests.
+
+To use this example, you must start an vLLM server with any model of your choice.
+
+```bash
+vllm serve Qwen/Qwen2.5-3B-Instruct
+```
+
+To serve a reasoning model, you can use the following command:
+
+```bash
+vllm serve deepseek-ai/DeepSeek-R1-Distill-Qwen-7B --reasoning-parser deepseek_r1
+```
+
+If you want to run this script standalone with `uv`, you can use the following:
+
+```bash
+uvx --from git+https://github.com/vllm-project/vllm#subdirectory=examples/online_serving/structured_outputs structured-output
+```
+
+See [feature docs](../../../features/structured_outputs.md) for more information.
+
+!!! tip
+    If vLLM is running remotely, then set `OPENAI_BASE_URL=<remote_url>` before running the script.
+
+## Usage
+
+Run all constraints, non-streaming:
+
+```bash
+uv run structured_outputs.py
+```
+
+Run all constraints, streaming:
+
+```bash
+uv run structured_outputs.py --stream
+```
+
+Run certain constraints, for example `structural_tag` and `regex`, streaming:
+
+```bash
+uv run structured_outputs.py --constraint structural_tag regex --stream
+```
+
+Run all constraints, with reasoning models and streaming:
+
+```bash
+uv run structured_outputs.py --reasoning --stream
+```