oss(langgraph): clarify baseUrl use (#1655)

- Clarify how to update the `baseUrl` parameter for custom host/port
configurations in Studio
- Add concrete example showing the URL format
- Fix casing from `baseURL` to `baseUrl` to match actual query parameter

Author: mdrxy

src/oss/langgraph/local-server.mdx

@@ -129,14 +129,18 @@ The `langgraph dev` command starts Agent Server in an in-memory mode. This mode
 >    - LangGraph Studio Web UI: https://smith.langchain.com/studio/?baseUrl=http://127.0.0.1:2024
 ```
 
-For an Agent Server running on a custom host/port, update the baseURL parameter.
+For an Agent Server running on a custom host/port, update the `baseUrl` query parameter in the URL. For example, if your server is running on `http://myhost:3000`:
+
+```
+https://smith.langchain.com/studio/?baseUrl=http://myhost:3000
+```
 
 <Accordion title="Safari compatibility">
-  Use the `--tunnel` flag with your command to create a secure tunnel, as Safari has limitations when connecting to localhost servers:
+    Use the `--tunnel` flag with your command to create a secure tunnel, as Safari has limitations when connecting to localhost servers:
 
-  ```shell
-  langgraph dev --tunnel
-  ```
+    ```shell
+    langgraph dev --tunnel
+    ```
 </Accordion>
 
 ## 7. Test the API
@@ -145,60 +149,60 @@ For an Agent Server running on a custom host/port, update the baseURL parameter.
 <Tabs>
     <Tab title="Python SDK (async)">
     1. Install the LangGraph Python SDK:
-      ```shell
-      pip install langgraph-sdk
-      ```
+        ```shell
+        pip install langgraph-sdk
+        ```
     2. Send a message to the assistant (threadless run):
-      ```python
-      from langgraph_sdk import get_client
-      import asyncio
-
-      client = get_client(url="http://localhost:2024")
-
-      async def main():
-          async for chunk in client.runs.stream(
-              None,  # Threadless run
-              "agent", # Name of assistant. Defined in langgraph.json.
-              input={
-              "messages": [{
-                  "role": "human",
-                  "content": "What is LangGraph?",
-                  }],
-              },
-          ):
-              print(f"Receiving new event of type: {chunk.event}...")
-              print(chunk.data)
-              print("\n\n")
-
-      asyncio.run(main())
-      ```
+        ```python
+        from langgraph_sdk import get_client
+        import asyncio
+
+        client = get_client(url="http://localhost:2024")
+
+        async def main():
+            async for chunk in client.runs.stream(
+                None,  # Threadless run
+                "agent", # Name of assistant. Defined in langgraph.json.
+                input={
+                "messages": [{
+                    "role": "human",
+                    "content": "What is LangGraph?",
+                    }],
+                },
+            ):
+                print(f"Receiving new event of type: {chunk.event}...")
+                print(chunk.data)
+                print("\n\n")
+
+        asyncio.run(main())
+        ```
     </Tab>
     <Tab title="Python SDK (sync)">
     1. Install the LangGraph Python SDK:
-      ```shell
-      pip install langgraph-sdk
-      ```
+        ```shell
+        pip install langgraph-sdk
+        ```
     2. Send a message to the assistant (threadless run):
-      ```python
-      from langgraph_sdk import get_sync_client
-
-      client = get_sync_client(url="http://localhost:2024")
-
-      for chunk in client.runs.stream(
-          None,  # Threadless run
-          "agent", # Name of assistant. Defined in langgraph.json.
-          input={
-              "messages": [{
-                  "role": "human",
-                  "content": "What is LangGraph?",
-              }],
-          },
-          stream_mode="messages-tuple",
-      ):
-          print(f"Receiving new event of type: {chunk.event}...")
-          print(chunk.data)
-          print("\n\n")
-      ```
+        ```python
+        from langgraph_sdk import get_sync_client
+
+        client = get_sync_client(url="http://localhost:2024")
+
+        for chunk in client.runs.stream(
+            None,  # Threadless run
+            "agent", # Name of assistant. Defined in langgraph.json.
+            input={
+                "messages": [{
+                    "role": "human",
+                    "content": "What is LangGraph?",
+                }],
+            },
+            stream_mode="messages-tuple",
+        ):
+            print(f"Receiving new event of type: {chunk.event}...")
+            print(chunk.data)
+            print("\n\n")
+        ```
     </Tab>
     <Tab title="Rest API">
     ```bash
@@ -226,9 +230,9 @@ For an Agent Server running on a custom host/port, update the baseURL parameter.
 <Tabs>
     <Tab title="Javascript SDK">
     1. Install the LangGraph JS SDK:
-      ```shell
-      npm install @langchain/langgraph-sdk
-      ```
+        ```shell
+        npm install @langchain/langgraph-sdk
+        ```
     2. Send a message to the assistant (threadless run):
       ```js
       const { Client } = await import("@langchain/langgraph-sdk");