fix: send error output to model when realtime tool call raises exception

[rmotgi1227]

Summary

Closes #3356.

When a known tool raised an exception (ToolTimeoutError with timeout_behavior="raise_exception", or any user-raised error), the exception propagated out of _handle_tool_call, got logged by _on_tool_call_task_done, but no RealtimeModelSendToolOutput was ever sent. The model waited for a function result that never arrived — effectively hanging the session for ~30 seconds until the server-side timeout fired.

The same class of problem was already fixed for the unknown-tool branch in #3287, which ensures the model always gets a reply. The known-tool exception branch was the remaining gap.

Fix: Wrap invoke_function_tool in a try/except inside _handle_tool_call. On failure, format an error string via default_tool_error_function and send it as a tool output with start_response=True so the model can recover and continue. The exception is not re-raised — the task completes normally and _stored_exception is not set, keeping the session alive.

Before/after for the three affected paths:

Path	Before	After
Known tool success	sends tool output ✓	unchanged ✓
Known tool exception/timeout	no output — model hangs ✗	sends error output, session continues ✓
Unknown tool	sends error output (fixed by #3287) ✓	unchanged ✓

Test plan

• Updated test_function_tool_timeout_raise_exception_propagates — no longer expects ToolTimeoutError to propagate; now verifies a model-visible error output is sent
• Updated test_function_call_event_timeout_raise_exception_enqueues_error — _stored_exception is now None (session stays alive); model receives tool output instead of hanging
• Updated test_function_tool_exception_handling — exception is now caught; model receives error output

uv run pytest tests/realtime/test_session.py -v   # 76 passed
uv run pytest tests/realtime/ -v                  # 244 passed
make lint
make typecheck

Issue number

Closes #3356.

Checks

• I've added new tests (if relevant)
• I've added/updated the relevant documentation (no doc changes needed)
• I've run make lint and make format
• I've made sure tests pass

[rmotgi1227]

Closing in favor of existing PRs #3393 and #3435 that address the same issue. Apologies for the duplicate.