fix(native): the app's browser sign-in no longer lands on the dashboard when the browser still holds an older TREK

A browser that ran TREK before 5.1.1 keeps that version's app in its service
worker. When the app opened /native-handoff, the worker answered it from its
cache with an app that has no such page, which sent the user to /, and the
sign-in ended on the dashboard in the browser instead of in the app.

The app now opens /api/auth/native/start, which every TREK service worker
passes to the server. That page takes the workers off the browser and
forwards to the handoff page. Until the sign-in is handed back, the web app
registers no service worker and does not reload for a new version: a tab
still open on the older TREK keeps its worker alive, and a registration or a
reload in the middle of the sign-in brought it back to answer the next page.

client/src/native/browserSignInFlag.test.ts

@@ -0,0 +1,29 @@
+import { afterEach, describe, expect, it } from 'vitest';
+import { BROWSER_SIGN_IN_KEY, BROWSER_SIGN_IN_TTL_MS, browserSignInRunning, endBrowserSignIn } from './browserSignInFlag';
+
+afterEach(() => localStorage.clear());
+
+describe('browserSignInRunning', () => {
+  it('FE-NATIVE-SIGNINFLAG-001: counts a mark from public/native-handoff.js for as long as a sign-in may take', () => {
+    const now = 1_000_000_000;
+    expect(browserSignInRunning(now)).toBe(false);
+
+    localStorage.setItem(BROWSER_SIGN_IN_KEY, String(now - 1000));
+    expect(browserSignInRunning(now)).toBe(true);
+
+    localStorage.setItem(BROWSER_SIGN_IN_KEY, String(now - BROWSER_SIGN_IN_TTL_MS));
+    expect(browserSignInRunning(now)).toBe(false);
+    // A clock set back, or anything that is no time at all.
+    localStorage.setItem(BROWSER_SIGN_IN_KEY, String(now + 60_000));
+    expect(browserSignInRunning(now)).toBe(false);
+    localStorage.setItem(BROWSER_SIGN_IN_KEY, 'soon');
+    expect(browserSignInRunning(now)).toBe(false);
+  });
+
+  it('FE-NATIVE-SIGNINFLAG-002: ends with the hand-back to the app', () => {
+    localStorage.setItem(BROWSER_SIGN_IN_KEY, String(Date.now()));
+    endBrowserSignIn();
+    expect(localStorage.getItem(BROWSER_SIGN_IN_KEY)).toBeNull();
+    expect(browserSignInRunning()).toBe(false);
+  });
+});