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/templates/index.tsx

@@ -96,7 +96,7 @@ function TemplatesListPage() {
       <div className="flex items-center justify-between">
         <h1 className="text-2xl font-bold">Lesson Plan Templates</h1>
         {canAdmin && (
-          <Button onClick={() => navigate({ to: '/lessons/templates/new', search: {} as Record<string, unknown> })}>
+          <Button onClick={() => navigate({ to: '/lessons/templates/new', search: { page: 1, limit: 25, q: undefined, sort: undefined, order: 'asc' as const } })}>
             <Plus className="mr-2 h-4 w-4" />New Template
           </Button>
         )}
@@ -126,7 +126,7 @@ function TemplatesListPage() {
         order={params.order}
         onPageChange={setPage}
         onSort={setSort}
-        onRowClick={(t) => navigate({ to: '/lessons/templates/$templateId', params: { templateId: t.id }, search: {} as Record<string, unknown> })}
+        onRowClick={(t) => navigate({ to: '/lessons/templates/$templateId', params: { templateId: t.id }, search: { page: 1, limit: 25, q: undefined, sort: undefined, order: 'asc' as const } })}
       />
     </div>
   )