[Bug] Xcode integration fails to load skills from ~/.claude/skills/

Bug Description
There's a skill loading bug in Xcode integration:

• Skills in ~/.claude/skills/ are discovered but not loaded into context
• The skill registry appears empty in Xcode's Claude agent
• The same skills work perfectly in Claude Code CLI
• Related to GitHub issue #22081

Steps to reproduce:

1. Install skill to ~/.claude/skills/tdd/
2. Open Xcode 26.3 with Claude integration
3. Ask "What skills are available?"
4. Result: Empty skill registry

Expected: Skills should appear in the registry like they do in CLI

Environment:

• Xcode 26.3
• macOS 26.2
• Claude Code 2.1.31

Environment Info

• Platform: darwin
• Terminal: Apple_Terminal
• Version: 2.1.31
• Feedback ID: bb03c2a9-9fd0-49fe-8561-7042cd39b629