fix: route OpenAI models through Responses API

[Maurice-aXeTech]

Problem

Flow always sends chat calls through LiteLLM's Chat Completions path. That remains valid for many models, but OpenAI is increasingly Responses-first; those models can reject or lose tool-call behavior when forced through /chat/completions.

There is currently no supported way to select the Responses API or deliberately retain Chat Completions for a proxy.

Change

• add an API Style setting to Flow Model: Auto, Responses, or Chat Completions
• route direct official openai/* models through LiteLLM's Responses bridge in Auto mode
• leave custom-base/proxy OpenAI connections and non-OpenAI providers on LiteLLM's existing/default route in Auto mode
• allow either route to be selected explicitly
• use the same routing helper for normal calls, streaming calls, persisted tool-result conversations, and Test Connection

The implementation continues to call litellm.completion(). It selects LiteLLM's built-in Responses bridge through the canonical openai/responses/<model> ID, so Flow keeps its current normalized ModelResponse, streaming, and tool-call handling instead of maintaining a second parser.

Compatibility

• existing Flow Model rows default to Auto
• non-OpenAI providers are unchanged
• OpenAI-compatible proxies with a custom Base URL are unchanged in Auto mode
• users can explicitly choose Chat Completions when required

Validation

• focused tests cover Auto routing, explicit overrides, tool calls, streaming, persisted assistant/tool messages, and Test Connection
• changed-file Ruff/format, Python compilation, JSON validation, and diff checks pass
• the Responses bridge was also smoke-tested against a local /v1/responses endpoint with a real function-call response

This is the first isolated change in a planned provider-connection cleanup; it has no dependency on the fork's Frappe 16-specific features.

[greptile-apps]

Confidence Score: 5/5

The PR appears safe to merge because no eligible blocking failure remains.

No blocking failure remains.

_{Reviews (2): Last reviewed commit: "fix: use valid Responses connection-test..." | Re-trigger Greptile}