docs: Update Claude Code instructions in README.md

Author: domdomegg

README.md

@@ -91,10 +91,10 @@ Chrome DevTools MCP will not start the browser instance automatically using this
 
 <details>
   <summary>Claude Code</summary>
-    Use the Claude Code CLI to add the Chrome DevTools MCP server (<a href="https://docs.anthropic.com/en/docs/claude-code/mcp">guide</a>):
+    Use the Claude Code CLI to add the Chrome DevTools MCP server (<a href="https://code.claude.com/docs/en/mcp">guide</a>):
 
 ```bash
-claude mcp add chrome-devtools npx chrome-devtools-mcp@latest
+claude mcp add chrome-devtools --scope user npx chrome-devtools-mcp@latest
 ```
 
 </details>