fix(handoffs): summarize all tool item types in nest_handoff_history

[adityasingh2400]

Summary

Extends the precedent set by #3095 (custom_tool_call) and #3386 (hosted_tool_call) into the sibling helper that powers RunConfig.nest_handoff_history. The _SUMMARY_ONLY_INPUT_TYPES set in src/agents/handoffs/history.py:30-37 only marked function_call, function_call_output, and reasoning as summarized-only. Every other tool kind the SDK can emit (computer, file_search, web_search, mcp_*, code_interpreter, image_generation, local_shell, shell, apply_patch, custom, hosted, tool_search) was included in the JSON conversation summary built by _format_transcript_item_json and re-forwarded verbatim as a raw RunItem in pre_handoff_items / input_items, duplicating it for the next agent.

Repro (passes pre-fix, fails post-fix without the new set entries):

>>> data = HandoffInputData(
...     input_history=(user_msg,),
...     pre_handoff_items=(custom_tool_call_run_item, custom_tool_output_run_item),
... )
>>> nested = nest_handoff_history(data)
>>> # Summary contains the tool call:
>>> "my_custom" in nested.input_history[0]["content"]
True
>>> # But the raw items also survive, so the next agent sees them twice:
>>> len(nested.pre_handoff_items)
2  # was expected to be 0

The fix expands _SUMMARY_ONLY_INPUT_TYPES to mirror the comprehensive list maintained by extensions.handoff_filters._remove_tool_types_from_input. The two lists exist for adjacent reasons (one for remove_all_tools, one for nest_handoff_history) but should agree on what counts as a tool item; the comment block documents that intent.

Test plan

• New tests test_nest_handoff_history_filters_hosted_tool_pre_items and test_nest_handoff_history_filters_hosted_tool_new_items in tests/test_extension_filters.py cover every hosted-tool call and output type for both the pre_handoff_items and new_items→input_items paths.
• uv run pytest tests/test_extension_filters.py — 42 passed (was 40, +2 regressions).
• uv run pytest tests/test_agent_runner.py tests/test_agent_runner_streamed.py -k handoff_history — 7 passed.
• make format, make lint, uv run mypy src/agents/handoffs/history.py tests/test_extension_filters.py — clean.

Issue number

N/A — found while auditing for the same gap that #3095 and #3386 fixed in the sibling remove_all_tools filter.

[seratch]

This may be relevant for some use cases, but it could be a breaking change for existing apps. Thus, we won't make this change.