feat: Add Codex-style OpenAI responses support

[dre8597]

Description

• add provider-level OpenAI headers for reused custom auth/session headers
• support Codex-style /responses requests by bridging system prompts into instructions and disabling store
• add a manual SSE path for Codex-compatible response streaming plus focused provider tests

Why

A downstream integration is currently carrying these changes as a local aisdk vendor patch in order to talk to ChatGPT Codex-compatible OpenAI endpoints. Upstreaming the behavior would let that local patch be removed once a release includes it.

Testing

• cargo test --features openai providers::openai::language_model::tests::

Type of Change

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• This change requires a documentation update

Checklist

• I have read the Contributing Guidelines.
• I have performed a self-review of my own code.
• I have commented my code, particularly in hard-to-understand areas.
• I have made corresponding changes to the documentation.
• My changes generate no new warnings.
• I have added tests that prove my fix is effective or that my feature works.
• New and existing unit tests pass locally with my changes.
• Any dependent changes have been merged and published in downstream modules.

[gaki2]

@ishaksebsib Can you review this PR?
I reviewed it and It looked good. But I'm not good at Rust. I'm sure you can review the details.