feat(unified-mailbox): enable search in the unified views

Enable text AND advanced search in all Unified Mailbox views (the per-role
mailboxes and the folder-selected All mail / Unread / Starred cross views). The
search input was hard-disabled for every unified view; the store fan-out already
supported text search.

- page.tsx: the search text input and the advanced-filter toggle are enabled for
  all unified views (only the scheduled view stays disabled). Clear-search also
  restores a cross view (not just per-role).
- Advanced filters now apply in cross views too: new advancedSearchCrossViewEmails
  ANDs the advanced filter (text + field conditions from buildJMAPFilter, built
  without an inMailbox clause) onto the cross-view membership. Per-role unified
  views keep using advancedSearchUnifiedEmails. Both honor the filter on the first
  page, on load-more, and on the folder-switch re-run. Fixes: an active Starred
  filter not applying after switching into a cross view, and the Unread filter in
  the Unread view returning nothing.
- Search persistence on folder switch: an active search is kept and re-run in the
  target view, preserving advanced filters. handleMailboxSelect picks
  advancedSearch when filters are set (normal, per-role unified, and cross views,
  after setting the unified state), text searchEmails when only a query is set,
  and browses otherwise. The scheduled view is the only view that resets the
  search on enter (unavailable there; setScheduledView clears searchQuery +
  searchFilters).

Account scope is intentionally left unrestricted in search (it already fanned out
across all accounts); the per-view folder selection still applies via
crossIncludedMailboxIds.

lib/__tests__/unified-mailbox-cross.test.ts

@@ -6,6 +6,7 @@ import {
   buildCrossFilter,
   getCrossUnreadTotal,
   fetchCrossViewEmails,
+  advancedSearchCrossViewEmails,
   resolveSourceFolderName,
   type UnifiedAccountClient,
 } from '@/lib/unified-mailbox';
@@ -203,3 +204,28 @@ describe('fetchCrossViewEmails', () => {
     expect(result.errors.get('bad')).toBe('boom');
   });
 });
+
+describe('advancedSearchCrossViewEmails', () => {
+  it('ANDs the advanced filter onto the cross-view membership', async () => {
+    const advancedSearchEmails = vi.fn().mockResolvedValue({ emails: [], total: 0, hasMore: false });
+    const a = makeAccount({ accountId: 'a', mailboxes: [mb('inbox', 'inbox')] }, { advancedSearchEmails });
+
+    await advancedSearchCrossViewEmails([a], 'all', { hasKeyword: '$flagged' }, 50, 0);
+
+    const [filter] = advancedSearchEmails.mock.calls[0];
+    expect(filter).toEqual({
+      operator: 'AND',
+      conditions: [{ inMailbox: 'inbox' }, { hasKeyword: '$flagged' }],
+    });
+  });
+
+  it('uses only the membership filter when the extra filter is empty', async () => {
+    const advancedSearchEmails = vi.fn().mockResolvedValue({ emails: [], total: 0, hasMore: false });
+    const a = makeAccount({ accountId: 'a', mailboxes: [mb('inbox', 'inbox')] }, { advancedSearchEmails });
+
+    await advancedSearchCrossViewEmails([a], 'all', {}, 50, 0);
+
+    const [filter] = advancedSearchEmails.mock.calls[0];
+    expect(filter).toEqual({ inMailbox: 'inbox' });
+  });
+});

lib/unified-mailbox.ts

@@ -465,6 +465,29 @@ export async function searchCrossViewEmails(
     ));
 }
 
+/**
+ * Like `searchCrossViewEmails`, but applies an advanced filter (text + field
+ * conditions from `buildJMAPFilter`, built WITHOUT an `inMailbox` clause) on top
+ * of the cross-view membership. `extraFilter` may be empty ({}), in which case
+ * only the membership filter is used (equivalent to a plain browse).
+ */
+export async function advancedSearchCrossViewEmails(
+  accounts: UnifiedAccountClient[],
+  view: CrossView,
+  extraFilter: Record<string, unknown>,
+  limit: number,
+  position: number,
+): Promise<UnifiedFetchResult> {
+  const hasExtra = Object.keys(extraFilter).length > 0;
+  return fanOutCrossQuery(accounts, (account, jmapAccountId, ids) => {
+    const membership = buildCrossFilter(view, ids);
+    const filter = hasExtra
+      ? { operator: 'AND', conditions: [membership, extraFilter] }
+      : membership;
+    return account.client.advancedSearchEmails(filter, jmapAccountId, limit, position);
+  });
+}
+
 /**
  * Returns the list of unified roles that exist in at least one account's
  * mailboxes.