feat: ALL IDE integration

[yashupadhyayy1]

This PR adds full support for Cursor IDE integration, including:

• Platform-aware hook installation for Cursor's hooks.json
• Robust binary resolution using login shell (sh -lc) wrappers
• Automatic Cursor protocol compatibility (JSON response formats)
• Updated built-in policies to support Cursor's tool naming conventions

Summary by CodeRabbit

• New Features

  • Multi-integration support: Cursor, Gemini CLI, GitHub Copilot, Codex; integration-aware hook handling and Copilot session viewing.

• CLI

  • New --integration flag for hook/policy commands, copilot-sync entry, improved signal/TTY hygiene and safer dist-binary resolution.

• UI

  • Activity filter by integration, Integration column/badges, project/session pages show Copilot sessions.

• Policies

  • Broader shell/tool detection, integration-specific hook outputs, new debug-prompt, and default policy config.

• Tests

  • New E2E and integration tests covering Cursor, Gemini, Copilot, and Codex.

• Tools

  • Codex trace extractor and Copilot session utilities.

• Docs

  • Changelog and integration plan added.