refactor: use Twilight AI SDK for model and provider connectivity tes… (#273)

* refactor: use Twilight AI SDK for model and provider connectivity testing

Replace hand-rolled HTTP probing with the Twilight AI SDK's built-in
Provider.Test() and TestModel() methods.

- Model test now runs Provider.Test() (connectivity + auth) followed by
  TestModel() (model availability) via the SDK
- Provider test auto-detects client_type from associated models and
  creates the correct SDK provider for accurate auth header handling
- Embedding models use a dedicated /embeddings endpoint probe since
  the SDK's chat Provider doesn't cover embedding APIs
- Latency measurement now covers the full test lifecycle
- Add TestStatusModelNotSupported for models not found by the provider
- Upgrade twilight-ai to v0.3.3-0.20260321100646-43c789b701dd which
  includes fallback probing for providers without GET /models/{id}

* fix: lint

apps/web/src/components/create-model/index.vue

@@ -63,11 +63,11 @@
               class="mt-2"
               :show-group-headers="false"
             >
-              <template #trigger="{ open, displayLabel }">
+              <template #trigger="{ open: isOpen, displayLabel }">
                 <Button
                   variant="outline"
                   role="combobox"
-                  :aria-expanded="open"
+                  :aria-expanded="isOpen"
                   class="w-full justify-between font-normal mt-2"
                 >
                   <span class="truncate">

apps/web/src/components/status-dot/index.vue

@@ -9,7 +9,7 @@
 import { computed } from 'vue'
 
 const props = withDefaults(defineProps<{
-  status: 'success' | 'error' | 'warning' | 'idle'
+  status?: 'success' | 'error' | 'warning' | 'idle'
 }>(), {
   status: 'idle',
 })