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Support the OpenAI Responses API
Background
OpenAI is moving to the responses API. Mostly they support the older chat completions API still, but in some cases they don't and we throw an error.
https://platform.openai.com/docs/guides/migrate-to-responses https://platform.openai.com/docs/api-reference/responses
Job to do
Add the new API to the OpenAI provider (goose/crates/goose/src/providers/openai.rs). Make this the default for actual OpenAI calls but allow for a switch in custom providers to choose between the old and the new, either by adding a protocol field to the DeclarativeProviderConfig or by having a different OpenAI provider type.
Acceptance
We can declare that this works if OpenAI works well (./scripts/test_providers.sh runs), you can create custom providers with the old and the new and that the current declarative providers still work and that we can upgrade them to the new protocol
Just to be sure it's not forgotten somewhere : Azure works the same way with OpenAi models. For example, Azure gpt-5-pro does not support chat completion
