fix: agent loop to support non-OpenAI providers by selecting correct response handler

[byteakp]

This PR fixes an issue where the agent loop would hang or fail when using non-OpenAI providers (e.g., Gemini), due to hardcoded assumptions about the /responses endpoint.

🔧 Changes Made:
Adjusted agent loop logic to dynamically select the correct response handler based on both the provider argument and project config.

Prevents attempts to call unsupported OpenAI-specific endpoints when using alternatives.

Ensures a smooth response flow across providers with varying endpoint structures.

🐛 Fixes:
Resolves #706

✅ Expected Behavior:
The agent responds correctly regardless of whether OpenAI or another provider (e.g., Gemini) is used.

No hangs, timeouts, or silent failures on unsupported endpoints.

[github-actions]

All contributors have signed the CLA ✍️ ✅
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[byteakp]

I have read the CLA Document and I hereby sign the CLA

[feelmypain]

Would be nice to push this ASAP after reviewing it.

[byteakp]

Hi @openai,
Could you please review my PR and provide feedback when possible? I’ve addressed the issue with the agent loop to support non-OpenAI providers and signed the CLA as requested. Let me know if there are any changes or further steps needed. Thank you!

[asadm]

Hey @openai, Is there a blocker on this one? I would LOVE to use this. Is there a plan to merge this? I am leaning pushing an alt npm package with this cherry picked otherwise.