Example: install, discover, and apply a CAO skill

Parent: #588

## Goal

Add a focused example for CAO's reusable skill lifecycle: install a skill, discover it, load its full guidance, apply it from an agent profile, and remove it cleanly.

The example should demonstrate CAO's skill system rather than relying on a skill only as hidden setup for another feature.

## Scope

- Add `examples/skills/` with a small self-contained skill, README, runnable entry point, compatible profile, fixture task, and focused tests.
- Run with a temporary `CAO_HOME_DIR` so the operator's installed skill catalog is not changed.
- Exercise `cao skills add`, `list`, and `remove`.
- Prove the skill is discoverable in the runtime catalog and retrievable through `load_skill`.
- Launch or simulate a profile that names the skill and demonstrate one observable behavior derived from the skill guidance.
- Document canonical versus installed copies, provider delivery differences, update/force behavior, and cleanup.
- Keep the skill deterministic and local; it must not require credentials or network access.

## Acceptance criteria

- [ ] The sample installs the bundled skill into an isolated CAO home.
- [ ] `cao skills list` reports the installed skill and `load_skill` returns its complete Markdown body.
- [ ] A profile can declare the skill and receive the intended catalog/guidance path for a supported provider.
- [ ] The fixture task has an observable result that demonstrates the skill was applied.
- [ ] Reinstall behavior is explicit and does not overwrite without the documented force path.
- [ ] Removal leaves the isolated catalog clean.
- [ ] Deterministic tests cover installation, discovery, loading, profile linkage, and cleanup.

## Non-goals

- Building a skill marketplace.
- Demonstrating every provider's native skill mechanism.
- Combining skill authoring with workflows, memory learning, or MCP Apps.

Create the self-contained example under examples/skills/, including the bundled skill, README, runnable entry point, compatible profile, fixture task, and focused tests. Start by tracing the existing cao skills add, list, and remove entry points and the load_skill path, then run the deterministic tests with a temporary CAO_HOME_DIR. Done means installation, discovery, loading, profile linkage, observable application, reinstall behavior, and cleanup are all demonstrated without network access.

Written by the indexing model from the issue text.