fix: replace invalid TanStack Router search casts with typed defaults

Newer TanStack Router enforces strict types on search params — 'search: {} as Record<string, unknown>' no longer satisfies routes with validateSearch. Replace all occurrences with the correct search shape for each destination route (pagination defaults for list routes, tab/field defaults for detail routes).

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

packages/admin/src/routes/_authenticated/lessons/schedule/index.tsx

@@ -49,7 +49,7 @@ function ScheduleHubPage() {
   const canAdmin = hasPermission('lessons.admin')
 
   function setTab(t: string) {
-    navigate({ to: '/lessons/schedule', search: { ...search, tab: t, page: 1 } as Record<string, unknown> })
+    navigate({ to: '/lessons/schedule', search: { ...search, tab: t, page: 1 } })
   }
 
   return (
@@ -152,7 +152,7 @@ function InstructorsTab({ canAdmin, search: _search }: { canAdmin: boolean; sear
         order={params.order}
         onPageChange={setPage}
         onSort={setSort}
-        onRowClick={(i) => navigate({ to: '/lessons/schedule/instructors/$instructorId', params: { instructorId: i.id }, search: {} as Record<string, unknown> })}
+        onRowClick={(i) => navigate({ to: '/lessons/schedule/instructors/$instructorId', params: { instructorId: i.id }, search: { page: 1, limit: 25, q: undefined, sort: undefined, order: 'asc' as const } })}
       />
     </div>
   )