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>

app/Models/Visit.php

@@ -94,6 +94,22 @@ class Visit extends Model
         return $this->hasMany(VisitStageAdvance::class, 'visit_id');
     }
 
+    /**
+     * Active or blocked advance for the visit's current workflow stage.
+     * Prefer this for eager-loaded queue board filtering (avoids N+1 currentAdvance queries).
+     */
+    public function currentStageAdvance(): HasOne
+    {
+        return $this->hasOne(VisitStageAdvance::class, 'visit_id')
+            ->ofMany(
+                ['id' => 'max'],
+                fn ($query) => $query->whereIn('status', [
+                    VisitStageAdvance::STATUS_ACTIVE,
+                    VisitStageAdvance::STATUS_BLOCKED,
+                ]),
+            );
+    }
+
     public function financialObligations(): HasMany
     {
         return $this->hasMany(FinancialObligation::class, 'visit_id');