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/new.tsx

@@ -45,7 +45,7 @@ function NewTemplatePage() {
       }),
     onSuccess: (template) => {
       toast.success('Template created')
-      navigate({ to: '/lessons/templates/$templateId', params: { templateId: template.id }, search: {} as Record<string, unknown> })
+      navigate({ to: '/lessons/templates/$templateId', params: { templateId: template.id }, search: { page: 1, limit: 25, q: undefined, sort: undefined, order: 'asc' as const } })
     },
     onError: (err) => toast.error(err.message),
   })
@@ -63,7 +63,7 @@ function NewTemplatePage() {
   return (
     <form onSubmit={handleSubmit} className="space-y-6 max-w-3xl">
       <div className="flex items-center gap-3">
-        <Button type="button" variant="ghost" size="sm" onClick={() => navigate({ to: '/lessons/templates', search: {} as Record<string, unknown> })}>
+        <Button type="button" variant="ghost" size="sm" onClick={() => navigate({ to: '/lessons/templates', search: { page: 1, limit: 25, q: undefined, sort: undefined, order: 'asc' as const } })}>
           <ArrowLeft className="h-4 w-4" />
         </Button>
         <h1 className="text-2xl font-bold">New Template</h1>
@@ -112,7 +112,7 @@ function NewTemplatePage() {
         <Button type="submit" disabled={mutation.isPending || !name.trim() || !allSectionsValid} size="lg">
           {mutation.isPending ? 'Creating...' : 'Create Template'}
         </Button>
-        <Button type="button" variant="secondary" size="lg" onClick={() => navigate({ to: '/lessons/templates', search: {} as Record<string, unknown> })}>
+        <Button type="button" variant="secondary" size="lg" onClick={() => navigate({ to: '/lessons/templates', search: { page: 1, limit: 25, q: undefined, sort: undefined, order: 'asc' as const } })}>
           Cancel
         </Button>
       </div>