[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_embeddings.ipynb

@@ -9,7 +9,7 @@
     "SGLang provides OpenAI-compatible APIs to enable a smooth transition from OpenAI services to self-hosted local models.\n",
     "A complete reference for the API is available in the [OpenAI API Reference](https://platform.openai.com/docs/guides/embeddings).\n",
     "\n",
-    "This tutorial covers the embedding APIs for embedding models. For a list of the supported models see the [corresponding overview page](../supported_models/embedding_models)\n"
+    "This tutorial covers the embedding APIs for embedding models. For a list of the supported models see the [corresponding overview page](../supported_models/retrieval_ranking/embedding_models.md)\n"
    ]
   },
   {
@@ -35,7 +35,7 @@
     "    --host 0.0.0.0 --is-embedding --log-level warning\n",
     "\"\"\")\n",
     "\n",
-    "wait_for_server(f\"http://localhost:{port}\")"
+    "wait_for_server(f\"http://localhost:{port}\", process=embedding_process)"
    ]
   },
   {
@@ -171,7 +171,7 @@
    "metadata": {},
    "source": [
     "## Multi-Modal Embedding Model\n",
-    "Please refer to [Multi-Modal Embedding Model](../supported_models/embedding_models)"
+    "Please refer to [Multi-Modal Embedding Model](../supported_models/retrieval_ranking/embedding_models.md)"
    ]
   }
  ],