feat: run conflict detection after Apply Changes

Run performConflictDetection automatically after the backend restarts from Apply Changes button to detect conflicts in newly installed packages

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <noreply@anthropic.com>

src/components/dialog/footer/ManagerProgressFooter.vue

@@ -102,6 +102,7 @@ import { computed, ref } from 'vue'
 import { useI18n } from 'vue-i18n'
 
 import DotSpinner from '@/components/common/DotSpinner.vue'
+import { useConflictDetection } from '@/composables/useConflictDetection'
 import { api } from '@/scripts/api'
 import { useComfyManagerService } from '@/services/comfyManagerService'
 import { useWorkflowService } from '@/services/workflowService'
@@ -118,6 +119,7 @@ const dialogStore = useDialogStore()
 const progressDialogContent = useManagerProgressDialogStore()
 const comfyManagerStore = useComfyManagerStore()
 const settingStore = useSettingStore()
+const { performConflictDetection } = useConflictDetection()
 
 // State management for restart process
 const isRestarting = ref<boolean>(false)
@@ -163,6 +165,9 @@ const handleRestart = async () => {
         await useCommandStore().execute('Comfy.RefreshNodeDefinitions')
 
         await useWorkflowService().reloadCurrentWorkflow()
+
+        // Run conflict detection on all installed packages after restart
+        await performConflictDetection()
       } finally {
         await settingStore.set(
           'Comfy.Toast.DisableReconnectingToast',