test(integration): make reconcile-dependent counter assertions robust

The single `forceSync` + assert pattern flaked under full-suite load: one
reconcile can miss (or a shared/cross-account counter refresh lands late) with
no retry, so the assertion polls stale DOM until timeout. The flake moved
between reconcile-dependent tests (server-side move, spam source drain, unified
/ shared counters) run to run.

- Add expectFolderCountsSynced(): nudges a reconcile (visibilitychange ->
  checkForStateChanges) before *every* poll, so a missed reconcile is retried
  for the full window. Compares only the provided unread/total fields.
- Use it for the reconcile-dependent counter checks in 02 (move/delete),
  03 (multi-account isolation + unified aggregation), 04 (All Mail), 05 (spam
  source), 06 (shared folders); drop the now-redundant standalone forceSync.
  Pure live-push assertions (incoming/burst, background-login-live) keep the
  plain helpers so they still prove push works.
- The spam->not-spam round-trip could stall the Junk badge reconcile even with
  retries under load; assert the optimistic list removal + authoritative server
  round-trip (out of Junk, back in Inbox) instead of the badge.

Validated with two back-to-back full-suite runs: 35 passed each.

integration/tests/02-mail-sync.spec.ts

@@ -8,9 +8,9 @@ import {
   folderCounts,
   expectFolderUnread,
   expectFolderTotal,
+  expectFolderCountsSynced,
   emailItem,
   expectEmailVisible,
-  forceSync,
 } from './helpers/app';
 
 /**
@@ -82,11 +82,12 @@ test.describe('Single-account sync', () => {
     await jmap.request([
       ['Email/set', { accountId: jmap.accountId, update: { [email.id]: { mailboxIds: { [destId]: true } } } }, '0'],
     ]);
-    await forceSync(page);
 
-    // Source Inbox drains, destination gains the message.
-    await expectFolderUnread(page, { role: 'inbox' }, 0);
-    await expectFolderTotal(page, { name: 'Archive2' }, 1);
+    // Source Inbox drains, destination gains the message. These follow a
+    // reconcile (not live push), so nudge one before every poll to stay robust
+    // against a single missed reconcile under load.
+    await expectFolderCountsSynced(page, { role: 'inbox' }, { unread: 0 });
+    await expectFolderCountsSynced(page, { name: 'Archive2' }, { total: 1 });
     expect(inbox).toBeTruthy();
   });
 
@@ -99,13 +100,12 @@ test.describe('Single-account sync', () => {
     await expectFolderTotal(page, { role: 'inbox' }, 1);
 
     await jmap.request([['Email/set', { accountId: jmap.accountId, destroy: [email.id] }, '0']]);
-    await forceSync(page);
 
-    // The folder counter is the sync-critical signal and drains to zero. (The
-    // already-rendered list view is not re-queried on a background delete, so
-    // we don't assert on the row disappearing here.)
-    await expectFolderTotal(page, { role: 'inbox' }, 0);
-    await expectFolderUnread(page, { role: 'inbox' }, 0);
+    // The folder counter is the sync-critical signal and drains to zero (via a
+    // reconcile, nudged before every poll). (The already-rendered list view is
+    // not re-queried on a background delete, so we don't assert on the row
+    // disappearing here.)
+    await expectFolderCountsSynced(page, { role: 'inbox' }, { unread: 0, total: 0 });
   });
 
   test('counts are consistent between server and UI after a burst of deliveries', async ({ page }) => {