fix(ui): poll for out-of-band email confirmation

An email link/code can be confirmed out of band: the recipient taps the
one-tap link in the email, which confirms in another browser/session. The
backend already publishes a `notify` `profile` re-fetch signal for this
(handlers_auth.go handleEmailConfirmLink), and the client re-fetches on it.

But the live stream is single-shot with no replay: a Mini App backgrounded
while the user is in their mail app tapping the link drops the stream and
misses the event (the gateway hub has no subscriber to deliver to), and the
reconnect on foreground does not re-sync — so the open code form stayed
until a manual reload. On Telegram Desktop the app is never backgrounded,
so the push works and there was no bug.

Add a client-side fallback: while an add-email confirmation is pending
(a code was sent, no email yet), poll `profile.get` on a 4s interval and on
foreground regain until the address lands; the effect stops as soon as the
email appears. The live push still updates instantly when foregrounded —
this only covers the backgrounded-miss gap.

Tests: a mock e2e attaches the email WITHOUT emitting a live event (new
window.__mock.clearEmail / confirmEmailOutOfBand seams), so it exercises the
poll, not the push, and asserts the code form collapses into the email row.
Docs: ARCHITECTURE.md §10 notes the single-shot gap + the poll fallback.

ui/src/lib/mock/client.ts

@@ -659,6 +659,17 @@ export class MockGateway implements GatewayClient {
     this.profile.email = email;
     return emptyLinked();
   }
+  // e2e hooks (window.__mock, see lib/gateway.ts): mockClearEmail drops the seeded email so the
+  // sign-in section offers the add-email flow; mockConfirmEmailOutOfBand attaches the address
+  // WITHOUT a live event — standing in for the one-tap confirm link opened in another browser,
+  // so the open code form must reflect it by polling the profile, not by a push.
+  mockClearEmail(): void {
+    this.profile.email = '';
+    this.emit({ kind: 'notify', sub: 'profile' });
+  }
+  mockConfirmEmailOutOfBand(email: string): void {
+    this.profile.email = email;
+  }
   async linkEmailMerge(email: string, _code: string): Promise<LinkResult> {
     this.profile.isGuest = false;
     this.profile.email = email;