## Background

faced the issue while implementing #13157 - for multiturn conversation,
the item Ids weren't properly being mapped within aisdk and there was a
mismatch between what we were sending to the openai api and what was
expected.

we were attching the same tool call id as the `tool-call` object to the
`tool-result` which caused duplicate ID found errors + incorrect ids
sent for certain parts

## Summary

- since the item_id for tool_search_output is propagated via
providerMetadata - we ensure the providerMetadata is preserved through
the UI stream.
- similar change needed for generate text as well

## Manual Verification

will be done in #13157 

## Checklist

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

## Background

faced the issue while implementing #13157 - for multiturn conversation,
the item Ids weren't properly being mapped within aisdk and there was a
mismatch between what we were sending to the openai api and what was
expected.

we were attching the same tool call id as the `tool-call` object to the
`tool-result` which caused duplicate ID found errors + incorrect ids
sent for certain parts

## Summary

- since the item_id for tool_search_output is propagated via
providerMetadata - we ensure the providerMetadata is preserved through
the UI stream.
- similar change needed for generate text as well

## Manual Verification

will be done in #13157 

## Checklist

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

This is an automated backport of #13157 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/openai/src/responses/convert-to-openai-responses-input.ts
Auto-merging packages/openai/src/responses/openai-responses-language-model.test.ts
CONFLICT (content): Merge conflict in packages/openai/src/responses/openai-responses-language-model.test.ts
Auto-merging packages/openai/src/responses/openai-responses-language-model.ts
Auto-merging packages/openai/src/responses/openai-responses-prepare-tools.ts
error: could not apply 156cdf0... feat(openai): add new tool search tool (#13157)
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"
```

---------

Co-authored-by: Aayush Kapoor <83492835+aayush-kapoor@users.noreply.github.com>
Co-authored-by: Aayush Kapoor <aayushkapoor34@gmail.com>