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/helpers/app.ts

@@ -272,6 +272,34 @@ export async function expectFolderTotal(page: Page, sel: FolderSelector, expecte
     .toBe(expected);
 }
 
+/**
+ * Assert a folder's counts, nudging a reconcile (visibilitychange ->
+ * checkForStateChanges) before *every* poll. Use for counters that update via
+ * reconcile rather than live SSE push — after a server-side move/delete, a
+ * mark-as-spam, or a shared-account change — where a single missed reconcile
+ * would otherwise flake. Only the provided fields are compared.
+ */
+export async function expectFolderCountsSynced(
+  page: Page,
+  sel: FolderSelector,
+  expected: { unread?: number; total?: number },
+  timeout = 45000,
+): Promise<void> {
+  await expect
+    .poll(
+      async () => {
+        await forceSync(page);
+        const c = await folderCounts(page, sel);
+        return {
+          ...(expected.unread !== undefined ? { unread: c.unread } : {}),
+          ...(expected.total !== undefined ? { total: c.total } : {}),
+        };
+      },
+      { timeout, intervals: [500, 1000, 1500, 2000, 2000, 3000] },
+    )
+    .toEqual(expected);
+}
+
 /** Click a folder row to select it. */
 export async function openFolder(page: Page, sel: FolderSelector): Promise<void> {
   await folderRow(page, sel).first().click();