…e-vertex (#11049)

## Background

Follow up to PR #10983 

## Summary

Added codemods for the breaking change highlighted in the migration
guide of the PR.

## Manual Verification

Tests and fixtures were added

## Checklist

- [x] Tests have been added / updated (for bug fixes / features)
- [x] 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)

…11073)

## Background

When using Azure OpenAI reasoning models via the Responses API, the SDK
currently only handles reasoning parts when their `providerOptions` live
under the `openai` key. Azure Responses, however, expose reasoning parts
and `providerMetadata` under the `azure` namespace. This mismatch causes
the SDK to log a warning about "non-OpenAI reasoning parts" and drop
encrypted reasoning traces instead of passing them through to the
client. See #10917.

## Summary

This PR makes the Responses provider options handling in
`@ai-sdk/openai` configurable and switches Azure Responses to use
`providerOptions.azure` so that reasoning parts and `providerMetadata`
stay in sync.

Concretely:

- **OpenAI provider**
Extend the Responses input conversion so that the provider options key
(`openai`, `azure`, etc.) is configurable instead of being hard-coded to
`openai`.
Keep the existing OpenAI behavior unchanged by continuing to use the
`openai` key by default.

- **Azure provider**
Update the Azure Responses integration to use the `azure` provider key
when reading/writing Responses `providerOptions`.
However, to maintain backward compatibility, `providerOptions.openai`
remains available.
This makes Azure reasoning parts and `providerMetadata.azure` consistent
and prevents encrypted reasoning traces from being treated as
unsupported "non-OpenAI reasoning".

- **Docs & migration**
Update the Azure provider docs to explain that the Responses API now
available `providerOptions.azure` `providerOptions.openai` and returns
`providerMetadata.azure`.
Add a migration note to the 6.0 migration guide describing the change
from `openai` → `azure` for Azure Responses.
  - `content/providers/01-ai-sdk-providers/04-azure.mdx`
  - `content/docs/08-migration-guides/24-migration-guide-6-0.mdx`

- **Examples & tests**
- Add ai-core examples for `reasoning.encrypted_content` for both OpenAI
and Azure Responses.
- Update existing Azure examples to use `providerOptions.azure` for
Responses.
- Add fixtures and tests to cover Azure/OpenAI Responses with encrypted
reasoning, ensuring we don’t regress on this behavior.
-
`packages/azure/src/__fixtures__/azure-reasoning-encrypted-content.1.chunks.txt`
-
`packages/azure/src/__fixtures__/azure-reasoning-encrypted-content.1.json`
-
`packages/openai/src/responses/__fixtures__/openai-reasoning-encrypted-content.1.chunks.txt`
-
`packages/openai/src/responses/__fixtures__/openai-reasoning-encrypted-content.1.json`
  - add test case.
- `packages/openai/src/responses/convert-to-openai-responses-input.ts`
-
`packages/openai/src/responses/openai-responses-language-model.test.ts`

## Manual Verification

- new tests in `examples/ai-core`
  -  `pnpm tsx src/generate-text/azure-reasoning-encrypted-content.ts`
  -  `pnpm tsx src/generate-text/openai-reasoning-encrypted-content.ts`
- `pnpm tsx
src/generate-text/azure-provider-options-name-openai-compatible.ts`
  -  `pnpm tsx src/stream-text/azure-reasoning-encrypted-content.ts`
  -  `pnpm tsx src/stream-text/openai-reasoning-encrypted-content.ts`
- `pnpm tsx
src/stream-text/azure-provider-options-name-openai-compatible.ts`


- fix existing tests and re-try in `examples/ai-core`.
  -  `pnpm tsx src/generate-text/azure-image.ts `
  -  `pnpm tsx src/generate-text/azure-responses-reasoning-summary.ts`
  -  `pnpm tsx src/stream-text/azure-fullstream-logprobs.ts`
  -  `pnpm tsx src/stream-text/azure-responses-reasoning-summary.ts`

- fix existing tests and re-try in `examples/next-openai`.
- `pnpm run dev` &
`http://localhost:3000/test-azure-code-interpreter-annotation-download`
(fix
examples/next-openai/app/api/chat-azure-code-interpreter-annotation-download/route.ts)

## Related Issues

Fixes #10917.

Reference #10983.
fix(google-vertex): allow 'vertex' as a key for providerOptions

---------

Co-authored-by: tsuzaki430 <tsuzaki430@users.noreply.github.com>