* 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
Acbox Liu
a7a36df705