PR #2068 dropped every reasoning item from input[] on the OAuth/codex path
(store=false). That silently discards encrypted_content -- the out-of-band
channel that carries reasoning context across turns under store=false --
degrading multi-turn agent reasoning with no visible error. Reported by
@neteroster on PR #2068.
The 404 that #2068 worked around ("Item with id 'rs_...' not found") is
triggered by the rs_* id lookup under store=false, not by the reasoning item
itself -- so the correct fix is to strip the id, not delete the item.
Verified end-to-end against the live chatgpt.com codex backend (gpt-5.5) and
a real OpenClaw container (api: openai-responses):
- bare rs_ id, no encrypted_content -> 404
- id stripped -> 200
- encrypted_content + id stripped -> 200, reasoning context preserved
- reasoning items require a summary field (missing -> 400)
- real OpenClaw multi-turn agent loop -> all /v1/responses 200, zero 404
Fix: keep the reasoning item, strip only the rs_* id (always, independent of
PreserveReferences), preserve encrypted_content/content/summary verbatim, and
backfill an empty summary when absent. Tool-call call_id pairing is untouched.
Also verified compaction_summary items (cmp_*, the other encrypted_content
carrier): they require encrypted_content (missing -> 400) and their id does not
404 when present (kept or stripped), so the existing generic path already
handles them safely -- no special-casing needed.
Adds regression tests for each verified reasoning contract.
Refs #1957, #2068