Error handling: require handler for abnormal finalization and use the handler in example apps.

_↴ Ported from [flutter/genui#740](https://github.com/flutter/genui/issues/740) — originally opened by [polina-c](https://github.com/polina-c) on 2026-02-20._
_Original labels: P2, front-line-handled, a: api-simplicity_

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Developer of the app should be enforced to handle not-successfull cycle.

## Expected behavior

Normal cycle:
- user sends message
- AI responds with one or more responses. The last response should be marked final by AI.

If something unexpected happened, application should:
1. Show nice message to user
2. Report technical details of the issue to the team via logs or other mechanism, if allowed by user

To make it easy for developer not to miss this handling, SDK should require to provide handler for abnormal finalization.

ai_primitives support finalization communication: https://github.com/flutter/genui/issues/696

dartantic_ai most likely does not support it yet (should we create issue for them?)

In addition, non-critical issues (like not respecting schema or providing not-unique id) should be discoverable and easy communicate for logging and telemetry.

## Actual behaviour

If there are issues, simple chat example shows nothing to user and just logs the issue:

```
flutter: FINE: 2026-02-19 20:58:36.766807: Attempt 4/4 for POST https://generativelanguage.googleapis.com/v1beta/models/gemini-3-flash-preview:streamGenerateContent?alt=sse
flutter: WARNING: 2026-02-19 20:58:36.780738: HTTP error retry exhausted after 3 attempts for POST https://generativelanguage.googleapis.com/v1beta/models/gemini-3-flash-preview:streamGenerateContent?alt=sse: ClientException with SocketException: Connection failed (OS Error: Operation not permitted, errno = 1), address = generativelanguage.googleapis.com, port = 443, uri=https://generativelanguage.googleapis.com/v1beta/models/gemini-3-flash-preview:streamGenerateContent?alt=sse
flutter: FINE: 2026-02-19 20:58:36.781240: Finalizing streaming orchestrator
flutter: SEVERE: 2026-02-19 20:58:36.781372: Error generating content
```

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### 2 comment(s) from the original issue

**[polina-c](https://github.com/polina-c)** commented on 2026-02-20:

@gspencergoog FYI

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**[polina-c](https://github.com/polina-c)** commented on 2026-02-21:

The mechanism should work well with failures of all types:
- LLM-request issue
- Parsing issue
- Renderong issue