Speed up Queue board loads by dropping sync and gate side effects.

Stop issuing missing tickets and refreshing financial gates on every GET;
eager-load advances, cap board rows, and cache specialty department maps.

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

tests/Feature/CareQueueBridgeTest.php

@@ -367,12 +367,20 @@ class CareQueueBridgeTest extends TestCase
             'reason' => 'Toothache',
         ]);
 
+        // Board GET must remain read-only; ticket backfill is explicit (Call next / artisan).
         $this->actingAs($this->owner)
             ->get(route('care.queue.index', ['branch_id' => $this->branch->id]))
             ->assertOk()
             ->assertSee('Toothache');
 
         $appointment = Appointment::query()->where('patient_id', $this->patient->id)->first();
+        $this->assertNull($appointment?->queue_ticket_uuid);
+
+        $issued = app(\App\Services\Care\CareQueueBridge::class)
+            ->syncMissingAppointmentTickets($this->organization->fresh(), (int) $this->branch->id, 10);
+        $this->assertSame(1, $issued);
+
+        $appointment = $appointment->fresh();
         $this->assertNotNull($appointment?->queue_ticket_uuid);
         $this->assertStringStartsWith('DEN', (string) $appointment->queue_ticket_number);
         $this->assertDatabaseHas('care_service_queues', [