chore: Clean up project root and update gitignore

- Remove Amazon extractor experiment files from root
- Add .claude/sync-cache.json to gitignore

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

.gitignore

@@ -4,6 +4,7 @@
 # Session state (user-specific)
 .claude/claude-state.json
 .claude/claude-progress.md
+.claude/sync-cache.json
 
 # Backup files
 *.bak