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.test.ts

@@ -0,0 +1,24 @@
+import { describe, expect, it } from 'vitest';
+import { resolveInstallBannerState } from './installBanner';
+
+describe('resolveInstallBannerState', () => {
+  it('returns null when already installed', () => {
+    expect(resolveInstallBannerState({ isInstalled: true, isStandalone: false, canInstall: true, isIos: true })).toBeNull();
+  });
+
+  it('returns null when running in standalone mode', () => {
+    expect(resolveInstallBannerState({ isInstalled: false, isStandalone: true, canInstall: true, isIos: true })).toBeNull();
+  });
+
+  it('returns prompt when install prompt is available', () => {
+    expect(resolveInstallBannerState({ isInstalled: false, isStandalone: false, canInstall: true, isIos: false })).toEqual({ variant: 'prompt' });
+  });
+
+  it('returns ios when on iOS without prompt', () => {
+    expect(resolveInstallBannerState({ isInstalled: false, isStandalone: false, canInstall: false, isIos: true })).toEqual({ variant: 'ios' });
+  });
+
+  it('returns null when no install option exists', () => {
+    expect(resolveInstallBannerState({ isInstalled: false, isStandalone: false, canInstall: false, isIos: false })).toBeNull();
+  });
+});