feat(07-uat): admin AI panel UX enhancements + DocumentCard status indicators

- GET /api/admin/ai-config/models — fetch model list from provider's /models endpoint
- POST /api/admin/ai-config/test-connection — replaced GET; accepts unsaved form
  values (api_key, base_url, model_name) so admins can test before saving
- TestConnectionRequest Pydantic model with provider_id validation
- SearchableModelSelect.vue — new reusable combobox; Teleport to body avoids
  overflow:hidden clipping; shows all models on open, filters only on typing;
  static "Enter manually" item always pinned at bottom; caches per provider
- AdminAiConfigTab: model name input replaced with SearchableModelSelect;
  testingProvider ref + spinner added to Test Connection button
- DocumentCard: processing spinner + "Classifying…", pending "Queued" badge,
  classification_failed badge; topics section only shown when status=ready
- FileManagerView: onUnmounted imported (polling wiring pending next session)

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

frontend/src/api/client.js

@@ -304,9 +304,17 @@ export function saveAiConfig(body) {
   })
 }
 
-export function testAiConnection(providerId) {
+export function testAiConnection(providerId, overrides = {}) {
+  return request('/api/admin/ai-config/test-connection', {
+    method: 'POST',
+    headers: { 'Content-Type': 'application/json' },
+    body: JSON.stringify({ provider_id: providerId, ...overrides }),
+  })
+}
+
+export function getAiModels(providerId) {
   return request(
-    '/api/admin/ai-config/test-connection?provider_id=' + encodeURIComponent(providerId),
+    '/api/admin/ai-config/models?provider_id=' + encodeURIComponent(providerId),
     { method: 'GET' }
   )
 }