Prevent failed SSE requests from masquerading as successful completions

The streaming API currently logs backend exceptions but still emits the
same `finish_reason: "stop"` + `[DONE]` terminator used for successful
responses. That makes a failed streamed request look successful to
OpenAI-compatible clients.

This keeps the fix narrow: track whether the stream backend failed and
suppress the success terminator in that case. A regression test locks in
the expected behavior.

Constraint: Keep the non-streaming response path untouched
Constraint: Follow up on the known limitation called out during PR #3222 review without redesigning the SSE protocol
Rejected: Introduce a custom SSE error event shape in the same patch | expands API surface and review scope
Confidence: high
Scope-risk: narrow
Reversibility: clean
Directive: If explicit streamed error events are added later, keep them distinct from the success stop+[DONE] terminator to preserve client retry semantics
Tested: PYTHONPATH=$PWD pytest -q tests/test_api_stream.py /Users/jh0927/Workspace/nanobot-validation-artifacts-2026-04-18/test_api_stream_error_regression.py
Not-tested: Full repository test suite
Related: #3260
Related: #3222

tests/test_api_stream.py

@@ -251,3 +251,30 @@ async def test_stream_with_session_id(aiohttp_client) -> None:
     )
     assert resp.status == 200
     assert captured_key == "api:my-session"
+
+
+@pytest.mark.skipif(not HAS_AIOHTTP, reason="aiohttp not installed")
+@pytest.mark.asyncio
+async def test_streaming_backend_failure_does_not_emit_success_terminator(aiohttp_client) -> None:
+    """Backend exceptions should not surface as a normal stop+[DONE] stream."""
+    agent = MagicMock()
+
+    async def boom(**kwargs):
+        raise RuntimeError("backend blew up")
+
+    agent.process_direct = boom
+    agent._connect_mcp = AsyncMock()
+    agent.close_mcp = AsyncMock()
+
+    app = create_app(agent, model_name="m")
+    client = await aiohttp_client(app)
+
+    resp = await client.post(
+        "/v1/chat/completions",
+        json={"messages": [{"role": "user", "content": "hi"}], "stream": True},
+    )
+
+    assert resp.status == 200
+    body = await resp.text()
+    assert '"finish_reason": "stop"' not in body
+    assert "[DONE]" not in body