Enable full PWA install experience in all web modes

- Add PWAInstallPrompt component for custom install UI and event handling
- Register PWAInstallPrompt in App.vue for global visibility
- Enable PWA features and install prompt in dev, test, and prod (vite.config.web.mts)
- Update service worker registration to work in all environments
- Update docs/build-web-script-integration.md with PWA install guidance and visual cues
- Add scripts/build-web.sh for unified web build/dev workflow

PWA is now installable and testable in all web environments, with clear user prompts and desktop support.

src/App.vue

@@ -1,6 +1,9 @@
 <template>
   <router-view />
 
+  <!-- PWA Install Prompt -->
+  <PWAInstallPrompt />
+
   <!-- Messages in the upper-right - https://github.com/emmanuelsw/notiwind -->
   <NotificationGroup group="alert">
     <div
@@ -334,6 +337,7 @@ import { Vue, Component } from "vue-facing-decorator";
 import { NotificationIface } from "./constants/app";
 import { PlatformServiceMixin } from "@/utils/PlatformServiceMixin";
 import { logger } from "./utils/logger";
+import PWAInstallPrompt from "@/components/PWAInstallPrompt.vue";
 
 interface Settings {
   notifyingNewActivityTime?: string;
@@ -341,6 +345,9 @@ interface Settings {
 }
 
 @Component({
+  components: {
+    PWAInstallPrompt
+  },
   mixins: [PlatformServiceMixin],
 })
 export default class App extends Vue {