Responses API mode (opt-in)

[anvztor]

Summary

Expose a BUB_USE_RESPONSES flag to route Bub/Republic through the OpenAI Responses API when required by upstream gateways.

Motivation

Bub currently uses Republic -> any-llm chat completions. Some OpenAI-compatible gateways only support /v1/responses, causing 404s. An opt-in flag keeps default behavior while enabling compatibility.

Proposed change

• Add BUB_USE_RESPONSES to settings and pass it into Republic's LLM.
• Document the new flag in README/env.example.

Backward compatibility

Default behavior remains chat completions unless BUB_USE_RESPONSES=true.

[anvztor]

Unit Test

$ uv --directory vendor/bub run python -m pytest -q
107 passed in 0.57s

E2E Test

I validated Responses routing locally with a mock /v1/responses server (see details in PR #67).