Issue cashier booth tickets when financial gates block service.

Pay-before-service holds now create a billing queue ticket (via an open bill) so cashiers can Call next / Serve; clearance completes the ticket and releases the clinical line as before.

Co-authored-by: Cursor <cursoragent@cursor.com>

app/Services/Care/Workflow/FinancialGateService.php

@@ -18,6 +18,9 @@ use App\Services\Care\CarePricingService;
  * A "before" gate blocks entry to the stage's service queue until the stage's
  * obligation is cleared (paid / authorized / waived / deferred). An "after"
  * gate never blocks entry but is created so the balance is collected at exit.
+ *
+ * When Care Queue Engine is enabled, WorkflowEngine / WorkflowQueueReleaseService
+ * place awaiting_payment visits on the billing (cashier) queue via an open bill.
  */
 class FinancialGateService
 {
@@ -143,7 +146,17 @@ class FinancialGateService
             'cleared_at' => now(),
         ])->save();
 
-        return $obligation;
+        $organization = Organization::query()->find($obligation->organization_id);
+        if ($organization) {
+            // Lazy resolve avoids a constructor cycle with WorkflowQueueReleaseService.
+            app(WorkflowQueueReleaseService::class)->completeCashier(
+                $organization,
+                $obligation->fresh(['bill']) ?? $obligation,
+                $method,
+            );
+        }
+
+        return $obligation->fresh() ?? $obligation;
     }
 
     public function void(FinancialObligation $obligation): FinancialObligation