Migrate OpenAI backends from Chat Completions API to Responses API

[NakaokaRei]

Summary

OpenAI has released the Responses API as the successor to the Chat Completions API. We should migrate OpenAIBackend (and OpenAIVisionBackend if applicable) to use the new API.

Current State

Both backends make direct URLSession requests to /v1/chat/completions with:

• messages array (system + user roles)
• response_format with json_schema for Structured Outputs
• Response parsing via choices[0].message.content

Relevant files:

• Sources/SwiftAutoGUI/OpenAIBackend.swift
• Sources/SwiftAutoGUI/OpenAIVisionBackend.swift (shares schema and parsing logic)

Proposed Changes

Migrate to POST /v1/responses with:

Chat Completions	Responses API
messages: [{role, content}]	instructions + input
response_format.json_schema	text.format
choices[0].message.content	output array
/v1/chat/completions	/v1/responses

Benefits

• Lower costs due to improved cache utilization
• previous_response_id for stateful conversation management
• Built-in tools (web search, code interpreter, etc.) available for future use
• Better reasoning model integration

Notes

• The Chat Completions API is not deprecated yet, so this is not urgent
• No SDK dependency change needed — we use raw URLSession calls
• baseURL parameter should be updated to default to the new endpoint path