Added onboarding + a lightweight install banner to both the mobile login screen and the settings screen, with Android/Chromium

install prompt support and iOS “Share → Add to Home Screen” guidance. Also added a small helper + tests to decide
  when/which banner variant should show, and shared copy in common.json.

resources/js/admin/mobile/lib/installBanner.ts

@@ -0,0 +1,28 @@
+export type InstallBannerVariant = 'prompt' | 'ios';
+
+export type InstallBannerState = {
+  variant: InstallBannerVariant;
+};
+
+export type InstallBannerInput = {
+  isInstalled: boolean;
+  isStandalone: boolean;
+  canInstall: boolean;
+  isIos: boolean;
+};
+
+export function resolveInstallBannerState(input: InstallBannerInput): InstallBannerState | null {
+  if (input.isInstalled || input.isStandalone) {
+    return null;
+  }
+
+  if (input.canInstall) {
+    return { variant: 'prompt' };
+  }
+
+  if (input.isIos) {
+    return { variant: 'ios' };
+  }
+
+  return null;
+}