[Docs] Sync docs_new with legacy docs and update migration redirects (#23337)

Co-authored-by: Mingyi <wisclmy0611@gmail.com>

docs_new/docs/basic_usage/openai_api_vision.mdx

@@ -7,36 +7,34 @@ SGLang provides OpenAI-compatible APIs to enable a smooth transition from OpenAI
 A complete reference for the API is available in the [OpenAI API Reference](https://platform.openai.com/docs/guides/vision).
 This tutorial covers the vision APIs for vision language models.
 
-SGLang supports various vision language models such as Llama 3.2, LLaVA-OneVision, Qwen2.5-VL, Gemma3 and [more](../supported-models).
+SGLang supports various vision language models such as Llama 3.2, LLaVA-OneVision, Qwen2.5-VL, Gemma3 and [more](../supported-models/multimodal_language_models).
 
 As an alternative to the OpenAI API, you can also use the [SGLang offline engine](https://github.com/sgl-project/sglang/blob/main/examples/runtime/engine/offline_batch_inference_vlm.py).
 
-
 ## Launch A Server
 
 Launch the server in your terminal and wait for it to initialize.
 
-
-
 ```python Example
 from sglang.test.doc_patch import launch_server_cmd
 from sglang.utils import wait_for_server, print_highlight, terminate_process
 
-vision_process, port = launch_server_cmd(
-    """
-python3 -m sglang.launch_server --model-path Qwen/Qwen2.5-VL-7B-Instruct --log-level warning
-"""
+example_image_url = "https://raw.githubusercontent.com/sgl-project/sglang/main/examples/assets/example_image.png"
+logo_image_url = (
+    "https://raw.githubusercontent.com/sgl-project/sglang/main/assets/logo.png"
 )
 
-wait_for_server(f"http://localhost:{port}")
+vision_process, port = launch_server_cmd("""
+python3 -m sglang.launch_server --model-path Qwen/Qwen2.5-VL-7B-Instruct --log-level warning
+""")
+
+wait_for_server(f"http://localhost:{port}", process=vision_process)
 ```
 
 ## Using cURL
 
 Once the server is up, you can send test requests using curl or requests.
 
-
-
 ```python Example
 import subprocess
 
@@ -56,7 +54,7 @@ curl -s http://localhost:{port}/v1/chat/completions \\
           {{
             "type": "image_url",
             "image_url": {{
-              "url": "https://github.com/sgl-project/sglang/blob/main/examples/assets/example_image.png?raw=true"
+              "url": "{example_image_url}"
             }}
           }}
         ]
@@ -76,8 +74,6 @@ print_highlight(response)
 
 ## Using Python Requests
 
-
-
 ```python Example
 import requests
 
@@ -92,9 +88,7 @@ data = {
                 {"type": "text", "text": "What’s in this image?"},
                 {
                     "type": "image_url",
-                    "image_url": {
-                        "url": "https://github.com/sgl-project/sglang/blob/main/examples/assets/example_image.png?raw=true"
-                    },
+                    "image_url": {"url": example_image_url},
                 },
             ],
         }
@@ -108,8 +102,6 @@ print_highlight(response.text)
 
 ## Using OpenAI Python Client
 
-
-
 ```python Example
 from openai import OpenAI
 
@@ -127,9 +119,7 @@ response = client.chat.completions.create(
                 },
                 {
                     "type": "image_url",
-                    "image_url": {
-                        "url": "https://github.com/sgl-project/sglang/blob/main/examples/assets/example_image.png?raw=true"
-                    },
+                    "image_url": {"url": example_image_url},
                 },
             ],
         }
@@ -144,8 +134,6 @@ print_highlight(response.choices[0].message.content)
 
 The server also supports multiple images and interleaved text and images if the model supports it.
 
-
-
 ```python Example
 from openai import OpenAI
 
@@ -160,13 +148,13 @@ response = client.chat.completions.create(
                 {
                     "type": "image_url",
                     "image_url": {
-                        "url": "https://github.com/sgl-project/sglang/blob/main/examples/assets/example_image.png?raw=true",
+                        "url": example_image_url,
                     },
                 },
                 {
                     "type": "image_url",
                     "image_url": {
-                        "url": "https://raw.githubusercontent.com/sgl-project/sglang/main/assets/logo.png",
+                        "url": logo_image_url,
                     },
                 },
                 {
@@ -183,7 +171,6 @@ response = client.chat.completions.create(
 print_highlight(response.choices[0].message.content)
 ```
 
-
 ```python Example
 terminate_process(vision_process)
 ```