feat(FN-4029): expose database health in API and store contracts

Adds database health endpoints to the API layer (FN-4029), exposing a new store health accessor through `api-node.ts` and `api/legacy.ts`, with aligned auth middleware integration tests and updated architecture documentation.

Fusion-Task-Id: FN-4029

packages/dashboard/app/api/legacy.ts

@@ -199,6 +199,11 @@ export interface DashboardHealthResponse {
   status: string;
   version: string;
   uptime: number;
+  database: {
+    healthy: boolean;
+    lastCheckedAt: string | null;
+    isRunning: boolean;
+  };
 }
 
 export function fetchDashboardHealth(): Promise<DashboardHealthResponse> {