…related multi-turn errors (#13262)

## Background

When using Gemini thinking models with image output, the Google API
returns `thought: true` on non-text parts (e.g. `inlineData` images).
The SDK correctly maps `thought: true` on text parts to `type:
'reasoning'`, but silently strips the flag from file parts. This causes
problems in multi-turn exchanges: the thought-image gets sent back as a
regular image, causing API errors because they're interpreted as regular
images but lack thought signatures (which per Google API are only
present on the non-reasoning images).

## Summary

Since we can't introduce a new part type without a spec change, this
preserves the `thought` flag on file parts via
`providerMetadata`/`providerOptions`.

- Add `thought: z.boolean().nullish()` to the `inlineData` member in the
provider-specific response schema
- In both `doGenerate` and `doStream`, propagate `thought: true` into
`providerMetadata` on file parts (alongside `thoughtSignature`)
- In `convertToGoogleGenerativeAIMessages`, read `thought` from
`providerMetadata` and send it back to the API on file parts

Function examples for `generate-text` and `stream-text` demonstrating
multi-step image generation with thinking are added, as well as an E2E
example that allows interactive multi-turn with reasoning output that
includes the images.

## Manual Verification

Test with the new examples to verify; for the E2E example making two
turns would result in an error without the `packages` fixes from this
PR.

## 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)

## Future Work

A provider-agnostic mechanism to distinguish thought content from output
content regardless of part type (as discussed in #12516) would be the
ideal long-term solution, removing the need for provider-specific
`providerMetadata` checks. However, this will require a spec change and
therefore is only an option for v7 - we should explore that further.

## Related Issues

Fixes #11461

…h and fix related multi-turn errors (#13281)

This is an automated backport of #13262 to the release-v6.0 branch. FYI
@felixarntz

Co-authored-by: Felix Arntz <felix.arntz@vercel.com>