test(e2e): a settings change persists on the server

The time-format choice is changed through the account settings and read
back after a reload, in a second browser context that shares only the
session cookie, and on /api/auth/me, on the settings journey's own account.

src/__tests__/e2e-critical-no-api-stub-guard.test.ts

@@ -50,7 +50,7 @@ const E2E = join(process.cwd(), "e2e");
  * somebody should see here. It counts title literals in the source, so a
  * title written once inside a loop counts once however many tests it names.
  */
-const CRITICAL_TEST_FLOOR = 14;
+const CRITICAL_TEST_FLOOR = 15;
 
 /** A test whose title literal carries the tag, however the call is spelled. */
 const CRITICAL_TEST =