feat(sp30): Dashboard Recent batches widget with billing outcome

- backend: GET /api/batches now returns acceptedCount/rejectedCount/
  pendingCount/billedTotal/topRejectionReason/hasProblem per item
  (one GROUP BY query + one ordered scan, no N+1)
- backend: 2 tests pin the 837p full-bucket case + the 835 zero case
- frontend: BatchSummary extended with 6 optional fields
  (backwards compat preserved)
- frontend: new RecentBatchesWidget renders one row per batch with
  status icon + billed total + accepted count + top rejection reason
- frontend: 837p rows show $ total + 'N/M accepted'; 835 rows show
  payment count (Remittance has no batch-level total_charge)
- frontend: full-width row between KPI tiles and Activity on the
  Dashboard; click navigates to /batches?batch=ID
- frontend: 3 component tests cover empty/clean/problem/835 branches

src/lib/api.ts

@@ -256,6 +256,25 @@ export interface BatchSummary {
    * instead of an extra round-trip to `/api/batches/{id}`.
    */
   claimIds: string[];
+  /**
+   * SP30: billing-outcome rollup computed server-side via one
+   * batched SQL aggregate (no N+1) so the Dashboard "Recent batches"
+   * widget can render one row per batch without a follow-up
+   * `/api/batches/{id}` call. All optional — pre-SP30 fixtures and
+   * tests that construct BatchSummary locally continue to work.
+   */
+  /** # claims whose state is paid / received / partial / reconciled. */
+  acceptedCount?: number;
+  /** # claims whose state is rejected / denied / reversed. */
+  rejectedCount?: number;
+  /** # claims whose state is submitted (or draft). */
+  pendingCount?: number;
+  /** SUM(charge_amount) across all claims (837P only; 0 for 835). */
+  billedTotal?: number;
+  /** Most-recent rejection_reason on the batch, truncated to 60 chars. */
+  topRejectionReason?: string | null;
+  /** True when rejectedCount > 0 OR any 277CA A4/A6/A7 claim. */
+  hasProblem?: boolean;
 }
 
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