Notify from the installed web app when a generation finishes.

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

pages/index.vue

@@ -5743,6 +5743,7 @@ async function generateExtension() {
   statusMessage.value = 'Extracting last frame & stitching extension...'
   startTimer('video')
   try {
+    await ensureGenerationNotifyPermission()
     const started = await $fetch<{ jobId: string; steps: number; hideThumbnail?: boolean; folderLocked?: boolean }>('/api/extend', {
       method: 'POST',
       body: {
@@ -6463,6 +6464,7 @@ async function editImage() {
   const extraPasses = editPassQueue.value.map(item => ({ prompt: item.prompt.trim() }))
   const hideOut = hideThumbnail.value
   try {
+    await ensureGenerationNotifyPermission()
     const body = new FormData()
     body.append('image', file.value)
     if (editRefFile.value) body.append('image2', editRefFile.value)
@@ -6679,6 +6681,7 @@ async function editImageV2() {
   const extraPasses = v2PassChaining.value ? editPassQueue.value.map(item => ({ prompt: item.prompt.trim() })) : []
   const hideOut = hideThumbnail.value
   try {
+    await ensureGenerationNotifyPermission()
     const body = new FormData()
     body.append('mode', v2Mode.value)
     body.append('task', v2Mode.value === 'generate' ? 't2i' : v2Mode.value === 'refine' ? 'refine' : v2Mode.value === 'compose' ? v2Task.value : 'scene')
@@ -6900,6 +6903,7 @@ async function generate() {
   const hideOut = hideThumbnail.value
   const folderLockedPref = false
   try {
+    await ensureGenerationNotifyPermission()
     const body = new FormData()
     if (file.value) body.append('image', file.value)
     if (inputStillId.value) body.append('stillId', inputStillId.value)
@@ -7132,6 +7136,7 @@ function applyEditEvent(payload: Record<string, any>, hidden: boolean, folderLoc
     scheduleLibraryRefresh()
     void pollComfyHealth()
     void refreshStudioQueue()
+    void notifyGenerationComplete('image')
     return
   }
 
@@ -7246,6 +7251,7 @@ function applyVideoEvent(payload: Record<string, any>, hidden: boolean, folderLo
       toast(locked
         ? 'Saved to the locked folder. Unlock it to view.'
         : 'New clip saved to the library')
+      void notifyGenerationComplete('video')
       return
     }
     if (locked) {
@@ -7277,6 +7283,7 @@ function applyVideoEvent(payload: Record<string, any>, hidden: boolean, folderLo
     scheduleLibraryRefresh()
     void pollComfyHealth()
     void refreshStudioQueue()
+    void notifyGenerationComplete('video')
     return
   }