Add an error event to InspectorClientEventMap so mid-session transport failures surface #1323

Background

useInspectorClient exposes status driven by the OAuth/XState machine inside InspectorClient. The status can transition connected → error when a transport dies mid-session (stdio subprocess crash, SSE stream drop, HTTP 5xx). Callers see the status flip but don't get the reason.

#1244 wired App.tsx to useInspectorClient and captures errorMessage only from client.connect() Promise rejection (handshake-only). A state-machine transition to "error" after a successful connect bypasses that path and leaves the UI's errorMessage stale (or unset).

Scope

• Add error: { detail: string; cause?: unknown } (or similar shape) to InspectorClientEventMap in core/mcp/inspectorClientEventTarget.ts.
• Dispatch from every code path inside core/mcp/inspectorClient.ts that sets status to "error" outside of an awaited promise.
• Expose lastError?: string on useInspectorClient's return type so consumers can render it without subscribing to the event directly.
• Update App.tsx to consume the new field instead of the connect() catch (or in addition to, for the handshake case).

Out of scope

• Reconnection UX. This is just about surfacing the reason.

Related

• Wire App.tsx to v2 core/ hook layer; remove demo stub from InspectorView #1244 (App.tsx wiring) — has a TODO marker at the connect catch block pointing here.