feat(plugin): enhance context management and skill invocation (#239)

* fix(shellcheck): declare and assign separately in router.sh (SC2155)

* feat(plugin): enhance context management and skill invocation

- Update .context-manifest.json to include profile and detailed source information.
- Revise context-scout.md to clarify context root discovery and navigation.
- Modify commands to replace deprecated skills with updated ones (brainstorming → approach, systematic-debugging → debugger).
- Streamline install-context.md for clarity and remove interactive profile selection.
- Improve oac-status.md to provide a more comprehensive status report.
- Add OAC system paths to session-start.sh for better context management.
- Remove obsolete skills and improve documentation for existing commands.