open_ai: Use responses API for all models (#54910) (cherry-pick to stable)

[zed-zippy]

Cherry-pick of #54910 to stable

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From the
docs:

Better performance: Using reasoning models, like GPT-5, with Responses
will result in better model intelligence when compared to Chat
Completions. Our internal evals reveal a 3% improvement in SWE-bench
with same prompt and setup.
Agentic by default: The Responses API is an agentic loop, allowing the
model to call multiple tools, like web_search, image_generation,
file_search, code_interpreter, remote MCP servers, as well as your own
custom functions, within the span of one API request.
Lower costs: Results in lower costs due to improved cache utilization
(40% to 80% improvement when compared to Chat Completions in internal
tests).
Stateful context: Use store: true to maintain state from turn to turn,
preserving reasoning and tool context from turn-to-turn.
Flexible inputs: Pass a string with input or a list of messages; use
instructions for system-level guidance.
Encrypted reasoning: Opt-out of statefulness while still benefiting from
advanced reasoning.
Future-proof: Future-proofed for upcoming models.

Self-Review Checklist:

• I've reviewed my own diff for quality, security, and reliability
• Unsafe blocks (if any) have justifying comments
• The content is consistent with the UI/UX
  checklist
• Tests cover the new/changed behavior
• Performance impact has been considered and is acceptable

Closes #ISSUE

Release Notes:

• Always use Responses API for OpenAI models