feat: add browser extension context debugging support

[Tasktivity]

Summary

Implements browser extension context debugging as requested in #96.

This PR adds the ability for AI coding assistants to inspect, debug, and interact with Chrome extension components including service workers, sidepanels, popups, and extension pages.

New Features

Feature	Description
--enableExtensions flag	Opt-in to enable extension debugging (avoids token overhead from enumerating extension contexts when not needed)
Extension pages in list_pages	Sidepanels, popups, options pages now visible
Service workers section	Extension service workers listed separately
open_extension_sidepanel	Opens sidepanel in detached popup window for debugging

Scope

This PR implements extension context debugging as requested in #96:

• Inspecting extension pages, sidepanels, popups, service workers
• Executing scripts in extension contexts
• Capturing console messages from extensions
• DOM interaction with extension UIs

Not Included (Future Work)

• Extension lifecycle management (install/uninstall/reload/list) - Planned for follow-up PR

Known Chrome Limitations

The following requested features are not technically feasible due to Chrome security restrictions:

• click_extension_icon - Browser toolbar is outside CDP's accessible viewport (puppeteer#2486)
• click_extension_context_menu - Context menus are browser UI elements, inaccessible via CDP

These are fundamental browser security constraints, not implementation gaps.

Testing

• 223/223 unit tests passing
• Real-world testing with TaskGator extension verified:
  • Sidepanel appears in list_pages ✓
  • select_page works for extension contexts ✓
  • take_snapshot captures extension UI ✓
  • click, fill, hover work on extension elements ✓
  • evaluate_script executes in extension context ✓
  • Settings navigation and theme toggle tested ✓

Usage

# Enable extension debugging
npx @anthropic-ai/claude-code-mcp chrome-devtools --enableExtensions

Partially Addresses #96

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[OrKoN]

Thanks for the PR but in its current form it does not align with how we plan to engineer it (e.g., re-using and modifying Puppeteer to provide better support for extension objects). We are already working on this feature including the features to support something like open_extension_sidepanel so stay tuned!

[Tasktivity]

Thanks for the PR but in its current form it does not align with how we plan to engineer it (e.g., re-using and modifying Puppeteer to provide better support for extension objects). We are already working on this feature including the features to support something like open_extension_sidepanel so stay tuned!

This would be great!