docs: Update README to reflect auto-open now works with authentication

- Removed outdated statement about auto-open being disabled with authentication
- Clarified that browser automatically opens with token pre-filled in URL
- Updated MCP_AUTO_OPEN_ENABLED description to note it works with authentication

The README now accurately reflects the improved developer experience where
authentication no longer prevents the browser from auto-opening.

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <[email protected]>

Author: felixweinberger

README.md

@@ -148,9 +148,9 @@ The MCP Inspector proxy server requires authentication by default. When starting
    http://localhost:6274/?MCP_PROXY_AUTH_TOKEN=3a1c267fad21f7150b7d624c160b7f09b0b8c4f623c7107bbf13378f051538d4
 ```
 
-This token must be included as a Bearer token in the Authorization header for all requests to the server. When authentication is enabled, auto-open is disabled by default to ensure you use the secure URL.
+This token must be included as a Bearer token in the Authorization header for all requests to the server. The inspector will automatically open your browser with the token pre-filled in the URL.
 
-**Recommended: Use the pre-filled URL** - Click or copy the link shown in the console to open the inspector with the token already configured.
+**Automatic browser opening** - The inspector now automatically opens your browser with the token pre-filled in the URL when authentication is enabled.
 
 **Alternative: Manual configuration** - If you already have the inspector open:
 
@@ -194,7 +194,7 @@ The MCP Inspector supports the following configuration settings. To change them,
 | `MCP_REQUEST_TIMEOUT_RESET_ON_PROGRESS` | Reset timeout on progress notifications                                                                       | true    |
 | `MCP_REQUEST_MAX_TOTAL_TIMEOUT`         | Maximum total timeout for requests sent to the MCP server (ms) (Use with progress notifications)              | 60000   |
 | `MCP_PROXY_FULL_ADDRESS`                | Set this if you are running the MCP Inspector Proxy on a non-default address. Example: http://10.1.1.22:5577  | ""      |
-| `MCP_AUTO_OPEN_ENABLED`                 | Enable automatic browser opening when inspector starts. Only as environment var, not configurable in browser. | true    |
+| `MCP_AUTO_OPEN_ENABLED`                 | Enable automatic browser opening when inspector starts (works with authentication enabled). Only as environment var, not configurable in browser. | true    |
 
 These settings can be adjusted in real-time through the UI and will persist across sessions.