fix: send realtime tool failure outputs

[pragnyanramtha]

Summary

Known realtime function tool and handoff failures could leave the model-visible tool call incomplete. When tool execution ran in the background, the SDK emitted a local RealtimeError, but it did not send a RealtimeModelSendToolOutput back to the model, so the realtime session could wait until the server-side tool timeout.

This PR keeps the existing exception path intact while completing the model-visible tool call:

• send RealtimeModelSendToolOutput(start_response=True) when a known function tool raises, including timeout_behavior="raise_exception"
• send the same model-visible failure output when a realtime handoff invocation raises or returns an invalid result
• preserve the propagated exception / stored exception behavior so application observers still receive the local error path
• add regression coverage for direct tool calls, async background tool calls, timeout exceptions, and handoff failures

Test plan

Passed:

• make format
• make format-check
• make lint
• uv run pytest tests/realtime/test_session.py::TestToolCallExecution::test_function_tool_timeout_raise_exception_propagates tests/realtime/test_session.py::TestToolCallExecution::test_function_call_event_timeout_raise_exception_enqueues_error tests/realtime/test_session.py::TestToolCallExecution::test_function_call_event_exception_sends_model_visible_output tests/realtime/test_session.py::TestToolCallExecution::test_handoff_tool_failure_sends_model_visible_output -q
• uv run pytest tests/realtime/test_session.py -q (78 passed)
• uv run pytest tests/realtime -q (246 passed)
• uv run mypy src/agents/realtime/session.py tests/realtime/test_session.py
• uv run pyright src/agents/realtime/session.py tests/realtime/test_session.py
• git diff --check

Attempted:

• make typecheck was attempted, but repo-wide checks failed outside this patch on existing optional-extra/baseline issues, including missing numpy, litellm, temporalio, sqlalchemy, boto3/botocore, and existing runloop sandbox type-form errors. The touched realtime files pass targeted mypy and pyright as listed above.

Issue number

Fixes #3356

Checks

• I've added new tests (if relevant)
• I've added/updated the relevant documentation (no docs change needed for this internal bug fix)
• I've run make lint and make format
• I've made sure tests pass

[Copilot]

Copilot encountered an error and was unable to review this pull request. You can try again by re-requesting a review.

[seratch]

this is a breaking change