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

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This is an automated backport of #14115 to the release-v6.0 branch. FYI @aayush-kapoor
This backport has conflicts that need to be resolved manually.

git cherry-pick output

Auto-merging packages/open-responses/src/open-responses-provider.ts
Auto-merging packages/open-responses/src/responses/open-responses-language-model.test.ts
CONFLICT (content): Merge conflict in packages/open-responses/src/responses/open-responses-language-model.test.ts
Auto-merging packages/open-responses/src/responses/open-responses-language-model.ts
CONFLICT (content): Merge conflict in packages/open-responses/src/responses/open-responses-language-model.ts
error: could not apply e69a836e5... feat(open-responses): add option to pass reasoning summary for OpenResponses (#14115)
hint: After resolving the conflicts, mark them with
hint: "git add/rm <pathspec>", then run
hint: "git cherry-pick --continue".
hint: You can instead skip this commit with "git cherry-pick --skip".
hint: To abort and get back to the state before "git cherry-pick",
hint: run "git cherry-pick --abort".
hint: Disable this message with "git config set advice.mergeConflict false"

[ghost]

🚀 Published in:

Package	Version
@ai-sdk/open-responses	1.0.11