feat(droid): add Factory AI Droid support

[skrabe]

Summary

• Adds RTK integration for Factory AI Droid CLI
• Factory Droid uses a PreToolUse hook system with the same hookSpecificOutput JSON format as Claude Code, with the shell tool named Execute instead of Bash
• Follows the Claude Code integration pattern: hook script + RTK.md + @RTK.md in AGENTS.md + settings.json patching

Changes

New files:

• hooks/droid/rtk-rewrite.sh — Shell hook script (delegates to rtk rewrite, same JSON protocol as Claude Code)
• hooks/droid/rtk-awareness.md — Slim RTK awareness instructions for hook-based usage
• hooks/droid/README.md — Integration docs

Modified files:

• src/main.rs — Added --droid flag to Init command, dispatch to run_droid(), wired into uninstall()
• src/hooks/init.rs — Added run_droid(), patch_droid_settings(), uninstall_droid(), resolve_droid_dir()
• README.md — Added Factory AI Droid to supported tools table and Quick Start

Install flow (rtk init -g --droid)

1. Writes hook script to ~/.factory/hooks/rtk-rewrite.sh (chmod 755)
2. Writes RTK.md to ~/.factory/RTK.md
3. Adds @RTK.md reference to ~/.factory/AGENTS.md (creates if missing, preserves existing content)
4. Patches ~/.factory/settings.json with PreToolUse hook entry (Execute matcher)

Uninstall flow (rtk init -g --droid --uninstall)

1. Removes ~/.factory/hooks/rtk-rewrite.sh
2. Removes ~/.factory/RTK.md
3. Removes @RTK.md line from ~/.factory/AGENTS.md (preserves other content)
4. Removes RTK hook entry from ~/.factory/settings.json

Test plan

• cargo fmt --all --check passes
• cargo clippy --all-targets — no new warnings
• cargo test — 1138 passed, 0 failed
• Manual: rtk init -g --droid --auto-patch installs all artifacts correctly
• Manual: idempotent — second install doesn't duplicate @RTK.md or settings entry
• Manual: rtk init -g --droid --uninstall removes all RTK artifacts
• Manual: existing AGENTS.md content and settings.json custom models preserved through install/uninstall cycle
• Manual: uninstall idempotent — second uninstall reports "nothing to remove"

[CLAassistant]

All committers have signed the CLA.