bug(vscode): dashboard episodes use a stale project root

[cedric013]

Problem

VS Code agents can produce episodic records while the native dashboard still shows every episode counter at zero.

The dashboard process inherits LEAN_CTX_PROJECT_ROOT from the extension host and /api/episodes hashes only that selected root. When the inherited value belongs to another workspace, the dashboard reads an empty store even though non-empty episode stores exist. Separately, MCP startup under WSL can accept /mnt/<drive>/Users/<user> as a markerless project root, so new episodes are persisted under a broad user-profile hash rather than the active repository.

Reproduction

1. Start VS Code with an inherited LEAN_CTX_PROJECT_ROOT for workspace A.
2. Open workspace B and run agents that record episodes.
3. Open the native lean-ctx dashboard from workspace B.
4. Observe /api/episodes scoped to workspace A and zero counters while episode stores for the agent session are non-empty.

Expected

• The VS Code dashboard is explicitly scoped to the active workspace folder.
• VS Code MCP configuration supplies ${workspaceFolder} as LEAN_CTX_PROJECT_ROOT.
• WSL-mounted Windows user profiles are rejected as broad project roots, while repositories below them remain valid.
• Multi-root detection never enumerates an unsafe broad root.

Scope

• pass the active workspace as --project when the extension launches the dashboard
• write LEAN_CTX_PROJECT_ROOT=${workspaceFolder} in VS Code MCP entries
• classify /mnt/<drive>/Users/<user> as broad/unsafe
• apply the shared broad-root guard before project and multi-root detection
• add focused regression coverage

Related

• Record agent episodic episodes reliably #1230 covers reliable episode recording
• MCP sessions stay rooted in markerless client cwd when extra roots allow the workspace #1258 covers rerooting markerless sessions after successful PathJail resolution

This issue covers the complementary VS Code launch/configuration and WSL broad-root paths.