feat(open-responses): add option to pass reasoning summary for OpenResponses

[aayush-kapoor]

Background

#13439

the open-responses provider did not parse the providerOptions passed for a model and was ignoring options such as reasoning.summary. it already had the api structure setup - ReasoningParam but wasn't

the original issue talks about AI SDK not parsing the reasoning effort but reasoning was added as a top level param and was taken care of

Summary

• import the parseProviderOptions function to parse the provider options passed along with an open-responses provider
• track the provider name set when using createOpenResponses so that provider option namespace uses the same value (and doesn't pass if not the same)
• include the reasoningSummary option in request

Manual Verification

verified by running the example examples/ai-functions/src/generate-text/open-responses/lmstudio-reasoning.ts

Checklist

• Tests have been added / updated (for bug fixes / features)
• Documentation has been added / updated (for bug fixes / features)
• A patch changeset for relevant packages has been added (for bug fixes / features - run pnpm changeset in the project root)
• I have reviewed this pull request (self-review)

Related Issues

fixes #13439