Responses adapter: reasoning continuity across mediated tool rounds (encrypted reasoning passthrough)

[mostlydev]

Follow-up to #31 / PR #32. The outbound Responses adapter is deliberately a compatibility layer, and for chat-shaped runners it is lossless in expressiveness — but not in model quality on multi-round tool use.

The limitation

The adapter sends store: false (preserving the chat/completions property that turns are not retained upstream) and drops reasoning output items when translating replies back to chat shape. Consequence: on every managed-mediation round, the model re-reasons from scratch — it never sees its own prior chain-of-thought. On exactly the models the adapter exists for (reasoning models), this costs quality and tokens on rounds ≥ 2.

Proposed fix

The Responses API supports stateless reasoning continuity without store: true:

1. request include: ["reasoning.encrypted_content"];
2. retain the encrypted reasoning items alongside the mediated round (the same hidden-state mechanism managedcontinuity uses for Anthropic thinking blocks);
3. replay them as input items on the next round.

No plaintext reasoning crosses into agent-visible state; governance surfaces are unaffected because the encrypted items live only in the adapter's hidden replay path.

For the record: what the adapter intentionally does not cover

Scoping notes from review, so the next reader doesn't rediscover them:

• Responses-native runners (e.g. Codex CLI speaks /v1/responses natively) still 404 at the mux. That — and only that — is the scenario that would justify a governed inbound /v1/responses route, with all governance surfaces re-proven for the second shape.
• Server-side tools (web_search, code_interpreter, computer use) are inexpressible in chat shape and out of scope for the adapter.
• True streaming: the adapter buffers and synthesizes SSE; time-to-first-token equals time-to-completion. Acceptable for tool-mediated turns, noticeable for long direct completions.