Specify tools array when calling /chat/completions endpoint

[freddygv]

Currently tool usage seems to only be specified via prompts.

That differs from how OpenAI expects function calling to happen, where tools are specified in a tools array:
https://platform.openai.com/docs/guides/function-calling?api-mode=chat&example=get-weather

This is likely leading to the issues where otherwise very smart models like o3 end up being awful at tool usage, despite OpenAI having trained them on it.

Calls to these endpoints should specify available tools with a JSON schema, as is done in the Codex CLI:
https://github.com/openai/codex/blob/f3bde217594e8be956a6583fde237f89fe2dd7c0/codex-cli/src/utils/responses.ts#L249-L289

Some open questions as someone not familiar with the codebase:

• Where/how should the JSON schema be defined so that it stays aligned with the system prompts? Should the system prompts move to JSON in general for consistency?
• Should tool instructions be removed from the system prompt for these models in favor of passing them via the /chat/completions calls?
• How do the models structure their responses after this change? What translation is needed when responses arrive?