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

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

docs_new/docs/basic_usage/native_api.ipynb

@@ -10,7 +10,7 @@
     "\n",
     "- `/generate` (text generation model)\n",
     "- `/get_model_info`\n",
-    "- `/get_server_info`\n",
+    "- `/server_info`\n",
     "- `/health`\n",
     "- `/health_generate`\n",
     "- `/flush_cache`\n",
@@ -49,7 +49,7 @@
     "    \"python3 -m sglang.launch_server --model-path qwen/qwen2.5-0.5b-instruct --host 0.0.0.0 --log-level warning\"\n",
     ")\n",
     "\n",
-    "wait_for_server(f\"http://localhost:{port}\")"
+    "wait_for_server(f\"http://localhost:{port}\", process=server_process)"
    ]
   },
   {
@@ -57,7 +57,7 @@
    "metadata": {},
    "source": [
     "## Generate (text generation model)\n",
-    "Generate completions. This is similar to the `/v1/completions` in OpenAI API. Detailed parameters can be found in the [sampling parameters](sampling_params)."
+    "Generate completions. This is similar to the `/v1/completions` in OpenAI API. Detailed parameters can be found in the [sampling parameters](sampling_params.md)."
    ]
   },
   {
@@ -140,7 +140,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "url = f\"http://localhost:{port}/get_server_info\"\n",
+    "url = f\"http://localhost:{port}/server_info\"\n",
     "\n",
     "response = requests.get(url)\n",
     "print_highlight(response.text)"
@@ -185,7 +185,15 @@
    "source": [
     "## Flush Cache\n",
     "\n",
-    "Flush the radix cache. It will be automatically triggered when the model weights are updated by the `/update_weights` API."
+    "Flush the radix cache. It will be automatically triggered when the model weights are updated by the `/update_weights` API.\n",
+    "\n",
+    "Parameters:\n",
+    "- `timeout` (query, float, default `0`, unit: seconds): Wait time for idle state before flushing. `0` means fail fast if not idle. When HiCache async operations are in-flight, a non-zero timeout allows the server to wait until idle before flushing, avoiding unnecessary 400 errors.\n",
+    "\n",
+    "```bash\n",
+    "# With timeout (wait up to 30s for idle state)\n",
+    "curl -s -X POST \"http://127.0.0.1:30000/flush_cache?timeout=30\"\n",
+    "```"
    ]
   },
   {
@@ -265,7 +273,7 @@
    "source": [
     "## Encode (embedding model)\n",
     "\n",
-    "Encode text into embeddings. Note that this API is only available for [embedding models](openai_api_embeddings) and will raise an error for generation models.\n",
+    "Encode text into embeddings. Note that this API is only available for [embedding models](openai_api_embeddings.ipynb) and will raise an error for generation models.\n",
     "Therefore, we launch a new server to server an embedding model."
    ]
   },
@@ -280,7 +288,7 @@
     "    --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)"
    ]
   },
   {
@@ -327,7 +335,7 @@
     "    --host 0.0.0.0 --disable-radix-cache --chunked-prefill-size -1 --attention-backend triton --is-embedding --log-level warning\n",
     "\"\"\")\n",
     "\n",
-    "wait_for_server(f\"http://localhost:{port}\")"
+    "wait_for_server(f\"http://localhost:{port}\", process=reranker_process)"
    ]
   },
   {
@@ -393,7 +401,7 @@
     "    --host 0.0.0.0 --log-level warning\n",
     "\"\"\")\n",
     "\n",
-    "wait_for_server(f\"http://localhost:{port}\")"
+    "wait_for_server(f\"http://localhost:{port}\", process=score_process)"
    ]
   },
   {
@@ -454,7 +462,7 @@
     "python3 -m sglang.launch_server --model-path Skywork/Skywork-Reward-Llama-3.1-8B-v0.2 --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=reward_process)"
    ]
   },
   {
@@ -518,7 +526,7 @@
     "    \"python3 -m sglang.launch_server --model-path Qwen/Qwen1.5-MoE-A2.7B --host 0.0.0.0 --expert-distribution-recorder-mode stat --log-level warning\"\n",
     ")\n",
     "\n",
-    "wait_for_server(f\"http://localhost:{port}\")"
+    "wait_for_server(f\"http://localhost:{port}\", process=expert_record_server_process)"
    ]
   },
   {
@@ -571,7 +579,7 @@
     "python3 -m sglang.launch_server --model-path qwen/qwen2.5-0.5b-instruct\n",
     "\"\"\")\n",
     "\n",
-    "wait_for_server(f\"http://localhost:{port}\")"
+    "wait_for_server(f\"http://localhost:{port}\", process=tokenizer_free_server_process)"
    ]
   },
   {