Inherited Personal skills appear as duplicate Project skills for folder projects

### Short summary

The Skills page lists Personal skills from `~/.agents/skills` again as Project skills for folder projects, although Copilot resolves them as inherited skills.

### Affected version or release

GitHub Copilot app [v1.1.14](https://github.com/github/app/releases/tag/v1.1.14) and GitHub Copilot CLI [v1.0.81-9](https://github.com/github/copilot-cli/releases/tag/v1.0.81-9)

### Installation context

GitHub Copilot app on macOS 26.5.2. [getsentry/dotagents](https://github.com/getsentry/dotagents) manages Personal skills in `~/.agents/skills`. The affected projects are non-Git folder projects.

### What happened?

The **Personal** section shows 22 skills from `~/.agents/skills`, as expected.

The **Project** section shows the same skills again under two folder projects. This presentation makes each inherited skill look like a separate project installation.

One project is `~/.agents`. The other is a separate non-Git workspace folder with no `agents.toml` file or project skill directory.

The native CLI identifies the workspace entries as inherited Personal skills:

```json
{
"name": "commit",
"source": "inherited",
"path": "/Users/example/.agents/skills/commit",
"enabled": true
}
```

`copilot skill list --json` reports no duplicate skill names in the effective catalog. This report concerns unclear UI classification and counting, not duplicate runtime loading.

The repeated rows also make the enable switches unclear. A user cannot tell whether a Project switch changes the Personal skill or creates a project-specific override.

### Steps to reproduce

1. Add one or more Personal skills under `~/.agents/skills`.
2. Add a non-Git folder project that has no project skill directory.
3. Open **Customize > Skills > All**.
4. Observe the skills in the **Personal** section.
5. Select the **Project** filter.
6. Observe the same skills under the folder project name.
7. Run `copilot skill list --json` from the folder project.
8. Observe that each affected skill has `"source": "inherited"` and a path under `~/.agents/skills`.

### Expected behavior

The Project section must not present inherited Personal skills as separate project installations.

If the Project section intentionally shows inherited availability, each row must use an **Inherited from Personal** label. The page must not count that row as another installed skill.

The enable switch must state whether it changes the Personal skill or creates a project-specific override.

### Additional context

The effective workspace catalog contains 35 unique skill names:

- 22 inherited skills
- 11 plugin skills
- 2 built-in skills

A duplicate-name scan returns an empty result. The problem is limited to the Customize page and its source labels or counts.

No screenshots are included because they contain confidential work information.

Related issues:

- https://github.com/github/app/issues/2814
- https://github.com/github/app/issues/3003
- https://github.com/github/app/issues/2718

Commencez dans Customize > Skills > All et comparez les entrées Project avec `copilot skill list --json` pour un projet de dossier, en vous concentrant sur les sources héritées et les nombres affichés. Le travail est terminé lorsque les Personal skills héritées ne sont pas présentées comme des installations distinctes, ou sont clairement étiquetées comme héritées, et que les interrupteurs d’activation expliquent si elles affectent les Personal skills ou créent des remplacements au niveau du projet.

Rédigé par le modèle d'indexation à partir du texte de l'issue.