Only notify legacy way if escalations not enabled

ee/app/services/concerns/ee/alert_management/alert_processing.rb

@@ -11,7 +11,7 @@ module EE
       def complete_post_processing_tasks
         super
 
-        notify_oncall if oncall_notification_recipients.present? && notifying_alert?
+        notify_oncall if !escalation_policies_available? && oncall_notification_recipients.present? && notifying_alert?
         process_escalations
       end
 
@@ -35,6 +35,10 @@ module EE
         end
       end
 
+      def escalation_policies_available?
+        ::Gitlab::IncidentManagement.escalation_policies_available?(project)
+      end
+
       def delete_pending_escalations
         # We use :delete_all here to avoid null constraint errors. (the default is :nullify).
         alert.pending_escalations.delete_all(:delete_all)

ee/spec/services/alert_management/process_prometheus_alert_service_spec.rb

@@ -55,7 +55,7 @@ RSpec.describe AlertManagement::ProcessPrometheusAlertService do
             stub_feature_flags(escalation_policies_mvc: project)
           end
 
-          include_examples 'oncall users are correctly notified of firing alert'
+          it_behaves_like 'does not send on-call notification'
           include_examples 'creates an escalation', 1
 
           context 'existing alert is now resolved' do

ee/spec/services/projects/alerting/notify_service_spec.rb

@@ -93,7 +93,7 @@ RSpec.describe Projects::Alerting::NotifyService do
           stub_feature_flags(escalation_policies_mvc: project)
         end
 
-        include_examples 'oncall users are correctly notified of firing alert'
+        it_behaves_like 'does not send on-call notification'
         include_examples 'creates an escalation', 1
       end