fix(ui): emit safe errors for failed SSE streams

[EfeDurmaz16]

What

A FastAPI route can start streaming an agent response before the upstream provider fails. In that case, to_sse() currently propagates the exception, so AI SDK UI receives a truncated response with no protocol error and no [DONE] marker.

This change:

• emits the existing UIErrorEvent for ordinary stream failures
• masks server details with An error occurred. by default
• adds an on_error callback for logging or a deliberate client-facing message
• closes recovered streams with [DONE]
• keeps to_stream(), cancellation, and generator shutdown behavior unchanged

Why

The existing web_agent example pipes to_sse() directly into FastAPI StreamingResponse. Once the response has started, an in-band AI SDK UI error chunk is the only structured way to report a provider failure to useChat.

This follows the concrete AI SDK UI interoperability direction discussed in #224.

Verification

• uv run --frozen pytest -q: 593 passed
• Ruff format and lint passed
• mypy and ty passed
• all repository example checks passed

Suggested release label: fix.

[vercel]

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