Settings screen empty after upgrading to v0.3.0

After upgrading `wordpress/wp-ai-client` from `v0.2.x` to `v0.3.0`, the AI Credentials settings screen at Settings → AI Credentials renders with no API key fields — just an empty form with a Save button.

<img width="658" height="237" alt="Image" src="https://github.com/user-attachments/assets/c978f9a1-90a1-40ec-b70b-32053f82b497" />

https://github.com/WordPress/wp-ai-client/pull/59