Pi engine: support OpenAI Responses API for reasoning with tools

[ilja]

Bug

The Pi engine’s generated OpenAI gateway currently hardcodes openai-completions.

OpenAI documents that, starting with GPT-5.4, Chat Completions does not support tool calling when reasoning_effort is anything other than none. Consequently, Pi workflows using tools with non-none reasoning fail before the first agent turn.

The API reports:

Function tools with reasoning_effort are not supported in /v1/chat/completions. To use function tools, use /v1/responses or set reasoning_effort to 'none'.

Reference: https://developers.openai.com/api/docs/guides/responses-vs-chat-completions

Expected behavior

Pi workflows should have a supported way to use openai-responses when tools and reasoning are enabled, either through automatic model-capability selection or explicit workflow configuration.

Acceptance criteria

• Pi can route OpenAI models through the Responses API.
• Tools work with non-none reasoning effort.
• Existing Chat Completions behavior remains available for compatible models.

[pelikhan]

@copilot there is already a way for the copilot agentic engine, reuse