✨ Improve third-party model metadata and reasoning continuity (#131)

## Summary
- Improve model picker metadata for third-party models by distinguishing
backend and model-family labels.
- Preserve reasoning continuity and expose richer model metadata across
provider discovery and request handling.
- Add regression coverage for display metadata, configuration, streaming
parts, response adaptation, normalization, capabilities, and pricing
behavior.

## Validation
- Branch contains three commits ahead of `main`.
- Tests and checks can run in CI for reviewer confirmation.