[Bug][UI] Cannot delete 'New Custom Provider' entry after saving without validation

[shangxinyu1]

Environment

Platform: macOS (per screenshot) / Windows
Version: 0.1.12-nightly.20260415
Component: AI Model Providers / Custom Provider Management

Steps to Reproduce

1. Go to Settings → AI Model Providers.
2. Click "+" to add a new custom provider.
3. Fill in some data and click Save (even if validation fails or fields are incomplete).
4. After saving, try to delete this newly created custom provider entry.

Actual Behavior

• After saving (even an incomplete entry), the "New Custom Provider" entry cannot be deleted.
• There is no delete button, or clicking delete has no effect.
• The invalid entry remains stuck in the provider list.

Expected Behavior

• Users should be able to delete any custom provider entry at any time, especially if it was created with incomplete information.
• The UI should allow cleanup of failed or test entries.

Impact

Severity: P1 (High)

• Users can get stuck with garbage/test entries in the provider list.
• Poor UX for experimenting with custom providers.
• No way to clean up invalid configurations.

Screenshot

[User-provided screenshot shows a 'Custom OpenAI-compatible' entry that cannot be removed after saving]

Root Cause Speculation

1. Save Action creates a permanent entry without proper ID or delete flag.
2. Delete button is conditionally hidden after the first save.
3. Backend validation issue prevents proper deletion if the record is in an inconsistent state.