ci(docs): Switch agentic workflows from Copilot to Claude engine (#5654)

## Summary

- Switch `docs-codebase-refresh` and `docs-codebase-update` GitHub
Agentic Workflows from the default Copilot engine to `engine: claude`
- Lock files recompiled via `gh aw compile`

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

Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com>

Author: dingsdax