docs: add Claude Code setup and update Claude Desktop flow for MCP server (#1375)

Author: xiaoyijun

docs/logto-cloud/logto-mcp-server.mdx

@@ -4,6 +4,9 @@ title: Logto MCP Server
 sidebar_position: 7
 ---
 
+import TabItem from '@theme/TabItem';
+import Tabs from '@theme/Tabs';
+
 # Logto MCP Server
 
 Logto MCP Server is a remote [MCP (Model Context Protocol)](https://modelcontextprotocol.io/) server. Add the URL to your AI application, sign in with your Logto Cloud account, and start talking to Logto.
@@ -21,13 +24,37 @@ More capabilities are coming soon, including sign-in experience configuration, R
 
 ## Set up in your AI application \{#set-up-in-your-ai-application}
 
+### Claude Code \{#claude-code}
+
+<Tabs>
+  <TabItem value="claude-mcp-add" label="claude mcp add">
+
+    ```bash
+    claude mcp add --transport http --client-id mcp-client --callback-port 8080 logto https://mcp.logto.io
+    ```
+
+  </TabItem>
+  <TabItem value="claude-mcp-add-json" label="claude mcp add-json">
+
+    ```bash
+    claude mcp add-json logto '{"type":"http","url":"https://mcp.logto.io","oauth":{"clientId":"mcp-client","callbackPort":8080}}'
+    ```
+
+  </TabItem>
+</Tabs>
+
+You can change `8080` to any available port on your machine.
+
+Then, run `/mcp` in Claude Code and follow the browser login flow to authenticate with your Logto Cloud account.
+
 ### Claude Desktop \{#claude-desktop}
 
 1. Open **Settings** from the main menu, navigate to **Connectors**, and click **Add custom connector**.
 2. Enter the name `Logto MCP Server` and the remote MCP server URL: `https://mcp.logto.io`.
 3. Expand **Advanced settings** and enter the OAuth Client ID: `mcp-client`. Click **Add**.
 4. In the **Connectors** list, find **Logto MCP Server** and click **Connect**.
-5. You will be redirected to the Logto Cloud sign-in page. Sign in and authorize to connect.
+5. You will first be redirected to the Claude web page. If you don't have an active session, sign in to your Claude account first.
+6. After signing in to Claude, you will be redirected to the Logto Cloud sign-in page. Sign in with your Logto Cloud account and authorize to connect.
 
 ### Cursor \{#cursor}