feat: PWA push notifications — service worker, VAPID, subscription management

- Add web-push VAPID backend with push_subscriptions table (migration 078)
- Backend push module with sendPushToUser/sendPushToRoom helpers
- Push routes: GET vapid-key, POST subscribe, DELETE unsubscribe
- Trigger push on new chat messages in direct/group rooms
- PWA manifest, service worker, and icons (72–512px)
- Frontend push lib: SW registration, subscribe/unsubscribe helpers
- Push API in api.ts, SW registered in main.tsx
- usePushSubscription hook for auto-subscribe on permission grant
- PushPermissionRow component in ChatWidget settings view

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

scripts/generate-icons.mjs

@@ -0,0 +1,22 @@
+import sharp from 'sharp'
+import { mkdirSync } from 'fs'
+
+mkdirSync('./public/icons', { recursive: true })
+
+const sizes = [72, 96, 128, 144, 152, 180, 192, 384, 512]
+
+const createSvg = (size) => {
+  const r = Math.round(size * 0.22)
+  const fontSize = Math.round(size * 0.36)
+  return `<svg xmlns="http://www.w3.org/2000/svg" width="${size}" height="${size}" viewBox="0 0 ${size} ${size}">
+  <rect width="${size}" height="${size}" rx="${r}" fill="#4F46E5"/>
+  <text x="${size/2}" y="${size/2 + fontSize*0.36}" font-family="Arial,sans-serif" font-weight="bold" font-size="${fontSize}" fill="white" text-anchor="middle">HS</text>
+</svg>`
+}
+
+for (const size of sizes) {
+  const svg = Buffer.from(createSvg(size))
+  await sharp(svg).png().toFile(`./public/icons/icon-${size}.png`)
+  console.log(`✓ icon-${size}.png`)
+}
+console.log('Done!')