Fix PWA shortcut icon on Windows

Allow unauthenticated access to favicon and manifest, generate favicon.ico, and add multi-size manifest icons.

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

scripts/prepare-public.mjs

@@ -28,14 +28,21 @@ function resetPublicDir() {
 }
 
 resetPublicDir()
+await import('./generate-icons.mjs')
 copyDir(path.join(root, 'assets'), path.join(publicDir, 'assets'))
 copyDir(path.join(root, 'images'), path.join(publicDir, 'images'))
 
 const siteDir = path.join(root, 'assets', 'site')
 if (fs.existsSync(siteDir)) {
+  const skipInPublicRoot = new Set(['apple-touch-icon.png'])
   for (const file of fs.readdirSync(siteDir)) {
+    if (skipInPublicRoot.has(file)) continue
     fs.copyFileSync(path.join(siteDir, file), path.join(publicDir, file))
   }
+  fs.copyFileSync(
+    path.join(siteDir, 'icon-512.png'),
+    path.join(publicDir, 'apple-touch-icon.png'),
+  )
 }
 
 console.log('[prepare-public] assets、images 与站点图标已同步到 .vitepress/public')