Skills registered through an extension's skillDirectories disappear after new_context, and restored sessions don't see them #5382

Describe the bug

An extension passes skillDirectories to joinSession. The skill works until the session clears its context with new_context (event session.context_cleared). Afterward the skill tool reports "Skill not found" and the skill is missing from the available list, while the extension process is still running and its tools still work. extensions_reload brings the skill back.

Sessions restored by /restart have the same gap: they list their skills before their extensions join, so they miss the skill until the extension calls session.rpc.skills.reload().

Affected version

GitHub Copilot CLI 1.0.107

Steps to reproduce the behavior

1. Add an extension that calls joinSession({ skillDirectories: ["<dir containing probe/SKILL.md>"] }).
2. In a session, call the skill tool with probe. It loads.
3. Call new_context.
4. Call the skill tool with probe. It reports "Skill not found". Personal and plugin skills are still listed.
5. Call extensions_reload, then the skill tool with probe. It loads again.

Expected behavior

A skill directory contributed by a joined extension stays registered for as long as the extension is joined, across context resets and restores.

Additional context

• macOS on Apple silicon (arm64).
• Seen on 2026-11-07. Five seconds after new_context, the skill tool reported the extension's skill not found while the extension process was running. After extensions_reload, the skill loaded.