Opt-in Responses API route for Bub/Republic integrations

[anvztor]

Background

We’re building an MVP task‑collaboration marketplace on top of Bub/Republic (DotTape). The product thesis is “verified output as the unit of value,” implemented via:

• Contract‑first tasks with explicit DoD and proof schema
• Proof Gate and reply‑after‑proof for settlement
• Event Tape for auditability and cost attribution
• Bub/Republic as the auditable executor layer

During integration with the sub2api gateway, we hit a hard block: the gateway only supports /v1/responses and does not support /v1/chat/completions (404 or upstream_error). Republic currently defaults to chat.completions, which prevents verification in this environment.

Request

Add an opt‑in Responses route in republic so Bub/Republic can call /v1/responses when configured, and ensure system/developer guidance is sent via Responses instructions instead of as system items in input.

Progress

• Implemented mapping of system/developer messages → instructions, and removed them from input_data for Responses calls.
• E2E test against the gateway now succeeds (previously 502).
• PR: feat: add opt-in Responses API mode #16

Why this matters

This change unblocks real‑world gateway integrations and keeps Republic aligned with Responses API semantics while preserving chat.completions as the default.