fix: repair stale defaultProviderId in storage on load

When the stored default provider ID doesn't match any loaded provider,
write back the corrected ID (providers[0].id) to storage so it doesn't
silently persist across sessions.

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

packages/browseros-agent/apps/agent/lib/llm-providers/useLlmProviders.ts

@@ -60,6 +60,15 @@ export function useLlmProviders(): UseLlmProvidersReturn {
           await defaultProviderIdStorage.setValue(loadedDefaultId)
         }
 
+        // Repair stale default ID that doesn't match any provider
+        const defaultExists = loadedProviders.some(
+          (p) => p.id === loadedDefaultId,
+        )
+        if (!defaultExists && loadedProviders.length > 0) {
+          loadedDefaultId = loadedProviders[0].id
+          await defaultProviderIdStorage.setValue(loadedDefaultId)
+        }
+
         setProviders(loadedProviders)
         setDefaultProviderId(loadedDefaultId)
       } catch {