Task: Implement the AppImage Double-Click Handler feature

TASK-DESCRIPTION

• Add the handle and handler commands to sources/tools/appimage_integrate.cpp.
• Implement the requirements in prompts/features/10-appimage-handler.md.
• Install the tools with make install.
• Register the handler with appimage-integrate handler install.
• Verify the default with xdg-mime query default for each AppImage MIME type.
• Run make test from the repository root.

TASK-OUTPUT

• Report the registration result, the recorded previous defaults, and the result of make test.

TASK-CONTEXT

• Feature requirements: prompts/features/10-appimage-handler.md.
• The user authorised registering this tool as the real *.AppImage default.
• Registration records the previous default so handler uninstall can restore it.
• AppImageLauncher owned the AppImage MIME definitions; a user-space copy at $XDG_DATA_HOME/mime/packages/appimage.xml preserves them if the package is removed.

TASK-FILES

• sources/tools/appimage_integrate.cpp — existing
• scripts/program-install.sh — existing
• Makefile — existing