VSCode extension "Web" tab doesn't show cloud session created from mobile app

Environment:

• VSCode version: 1.137.0
• Claude Code extension: 2.1.274 (darwin-arm64)
• OS: macOS (Darwin 25.6.0)

Description:
A cloud session created via the Claude mobile app does not appear in the VSCode extension's cloud sessions ("Web") tab, even though it's visible from the mobile app itself and confirmed to exist on claude.ai/code.

Steps to reproduce:

1. Create a new cloud session from the Claude mobile app, associated with a GitHub repo.
2. Open that same repo's folder in VSCode with the Claude Code extension installed.
3. Open the extension's session history / "Web" (cloud sessions) tab.
4. Expected: the new cloud session appears in the list.
5. Actual: it does not appear — the tab only offers to start a new cloud session.

Confirmed during troubleshooting:

• Same Claude account signed in on both VSCode extension and mobile app (verified via /usage).
• Only one Claude account in use — no account/org mismatch.
• The correct GitHub repo (matching the one the cloud session is associated with) is open in VSCode.
• Session is confirmed to exist and is visible at claude.ai/code.
• Reloading the VSCode window did not resolve it.
• Fully quitting and reopening VSCode did not resolve it.
• Extension is up to date (2.1.274).
• Signing out/in via the account switcher did not force a refresh (no explicit force-refresh/logout option available from the extension UI).

Impact: Cloud sessions started on mobile are unreachable from the VSCode extension, breaking the intended cross-client continuity of cloud sessions.