[BUG] Sessions created in VS Code extension not visible in web/FleetView UI — asymmetric session visibility

Description

Sessions created in the VS Code extension are not visible in the web/FleetView UI, but sessions created in the web UI are visible in the VS Code extension. The sync is one-directional.

Expected behaviour

Session visibility should be bidirectional — if one surface can see sessions from the other, both surfaces should see each other's sessions.

Actual behaviour

• ✅ Sessions created in the web/FleetView UI → visible in VS Code extension
• ❌ Sessions created in VS Code extension → not visible in web/FleetView UI

Steps to reproduce

1. Start a new session in the VS Code Claude Code extension and do some work.
2. Open the web/FleetView UI.
3. Browse the session list — the VS Code session does not appear.
4. Create a session in the web UI, then check VS Code — that session does appear.

Environment

• Platform: macOS
• Surface: VS Code extension + web/FleetView UI

Hypothesis

The VS Code extension likely writes sessions to a different storage location or with a different tag/marker than the web UI expects. The web UI reads from its own storage (which the extension also reads), but does not read from wherever the extension writes its sessions — resulting in the asymmetry.