Ollama recently added Responses API support via its OpenAI-compatible
endpoint (/v1/responses). This adds a proxy endpoint to the Ollama
router that forwards requests to Ollama's /v1/responses, applying
the same model resolution, access control, and prefix_id handling
used by the existing /v1/chat/completions and /v1/messages proxies.
Uses a typed ResponsesForm Pydantic model with required model field
and extra='allow' for forward compatibility, consistent with other
endpoint schemas in the file.
This allows API consumers (Codex, Claude Code, etc.) to use the
Responses API directly with Ollama-hosted models without requiring
a separate OpenAI-compatible connection.