The max-iterations summary path (`handle_max_iterations`) hand-builds its
message list and calls `chat.completions.create()` directly, bypassing
`ChatCompletionsTransport.convert_messages()`. It only popped
("reasoning", "finish_reason", "_thinking_prefill"), so `tool_name` (SQLite
FTS bookkeeping), the `codex_*` reasoning carriers, and other internal
`_`-prefixed scaffolding leaked to the wire.
Strict OpenAI-compatible gateways (Fireworks-backed OpenCode Go, Mistral,
Moonshot/Kimi) reject these with HTTP 400 "Extra inputs are not permitted,
field: 'messages[N].tool_name'", so a long tool-using session that exhausts
the iteration budget fails to summarise instead of returning the result.
Mirror convert_messages() in this path: also drop tool_name,
codex_reasoning_items, codex_message_items, and every `_`-prefixed key.
Copy-on-write is already in place, so internal history keeps the fields for
FTS / Codex-fallback.
Adds a regression test to TestHandleMaxIterations asserting the summary
request carries none of the schema-foreign keys (fails on main, passes here).
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