fix(run): persist the max-turns handler output to the session

[LeSingh1]

Summary

When a max_turns run error handler returns a final output with include_in_history=True, the non-streamed runner never wrote the synthesized assistant message to the session.

save_result_to_session uses run_state._current_turn_persisted_item_count as a slice offset into the new_items list it is given. That is only valid when the caller passes the cumulative turn item list. The max-turns block passes a fresh one-item list [synthesized_item], and it runs before the per-turn counter reset, so any previous turn that persisted at least one item makes already_persisted >= len(new_items) and nothing is saved at all. The next run on that session has no record of the assistant's answer.

The streamed path resets the counter before the max-turns check and persists the item correctly, so the two paths silently disagreed on what ends up in history.

Fix: pass run_state=None with an explicit reasoning_item_id_policy at that call site, matching what save_resumed_turn_items already does for the same "this is not a cumulative turn list" situation. Per-turn counter semantics are untouched everywhere else.

Test plan

Added a shared helper in tests/test_max_turns.py that runs one tool turn, trips max_turns=1 with a handler returning include_in_history=True, and asserts the resulting SQLiteSession contents.

• non-streamed: fails on main (session is missing the final message), passes with the fix
• streamed twin: passes both before and after, locking in the alignment between the two paths

tests/test_max_turns.py → 22 passed. tests/test_agent_runner.py tests/test_run_state.py tests/memory tests/test_hitl_session_scenario.py → 579 passed. .agents/skills/code-change-verification/scripts/run.sh passed.

Issue number

N/A — found while auditing session persistence parity between the streamed and non-streamed runners.

Checks

• I've added new tests, if relevant
• I've run .agents/skills/code-change-verification/scripts/run.sh
• I've confirmed all verification steps pass
• If using Codex, I've run /review before submitting this PR