…e google_search_retrieval implementation (#13070)

This is an automated backport of #12926 to the release-v5.0 branch. FYI
@felixarntz
~~This backport has conflicts that need to be resolved manually.~~
Conflicts resolved.

### `git cherry-pick` output

```
Auto-merging content/providers/01-ai-sdk-providers/15-google-generative-ai.mdx
CONFLICT (content): Merge conflict in content/providers/01-ai-sdk-providers/15-google-generative-ai.mdx
CONFLICT (file location): examples/ai-functions/src/generate-text/google/image-search.ts added in 2565e70 (feat(google): add support for image search, replace obsolete google_search_retrieval implementation (#12926)) inside a directory that was renamed in HEAD, suggesting it should perhaps be moved to examples/ai-core/src/generate-text/image-search.ts.
CONFLICT (file location): examples/ai-functions/src/generate-text/google/search-types.ts added in 2565e70 (feat(google): add support for image search, replace obsolete google_search_retrieval implementation (#12926)) inside a directory that was renamed in HEAD, suggesting it should perhaps be moved to examples/ai-core/src/generate-text/search-types.ts.
CONFLICT (file location): examples/ai-functions/src/stream-text/google/image-search.ts added in 2565e70 (feat(google): add support for image search, replace obsolete google_search_retrieval implementation (#12926)) inside a directory that was renamed in HEAD, suggesting it should perhaps be moved to examples/ai-core/src/stream-text/image-search.ts.
CONFLICT (file location): examples/ai-functions/src/stream-text/google/search-types.ts added in 2565e70 (feat(google): add support for image search, replace obsolete google_search_retrieval implementation (#12926)) inside a directory that was renamed in HEAD, suggesting it should perhaps be moved to examples/ai-core/src/stream-text/search-types.ts.
Auto-merging packages/google/src/google-generative-ai-language-model.test.ts
CONFLICT (content): Merge conflict in packages/google/src/google-generative-ai-language-model.test.ts
Auto-merging packages/google/src/google-generative-ai-language-model.ts
Auto-merging packages/google/src/google-prepare-tools.test.ts
Auto-merging packages/google/src/google-prepare-tools.ts
CONFLICT (content): Merge conflict in packages/google/src/google-prepare-tools.ts
Auto-merging packages/google/src/tool/google-search.ts
CONFLICT (content): Merge conflict in packages/google/src/tool/google-search.ts
error: could not apply 2565e70... feat(google): add support for image search, replace obsolete google_search_retrieval implementation (#12926)
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: Felix Arntz <felix.arntz@vercel.com>

…arch with multimodal output (#13171)

## Summary

This helps test and verify that thought signatures now work correctly
end-to-end, for both images and web search and image search sources,
including in multi-turn content.

## Manual Verification

Did some extensive testing with these two new examples - everything
works as expected.

## 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)
- [x] I have reviewed this pull request (self-review)

## Related Issues

Follow up to #12926

…arch with multimodal output (#13171)

## Summary

This helps test and verify that thought signatures now work correctly
end-to-end, for both images and web search and image search sources,
including in multi-turn content.

## Manual Verification

Did some extensive testing with these two new examples - everything
works as expected.

## 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)
- [x] I have reviewed this pull request (self-review)

## Related Issues

Follow up to #12926