Add Platform Integration Guide for claude-mem worker service

- Introduced comprehensive documentation for integrating claude-mem into VSCode extensions, IDE plugins, and CLI tools.
- Detailed worker service basics, including environment variables and build commands.
- Provided an overview of worker architecture and request flow.
- Documented API reference for session lifecycle, data retrieval, search operations, and settings configuration.
- Included integration patterns, error handling strategies, and development workflow guidelines.
- Added critical implementation notes and additional resources for developers.

docs/public/docs.json

@@ -55,7 +55,8 @@
         "pages": [
           "configuration",
           "development",
-          "troubleshooting"
+          "troubleshooting",
+          "platform-integration"
         ]
       },
       {