feat(vue): add useObject support for Vue

[tom-auger]

Background

Adds useObject support to the Vue package.

Summary

• Added experimental_useObject to the Vue package, following the same pattern as the React version.
• Added unit tests similar to the corresponding React tests.
• Added example page to the nuxt-openai example project
• Updated the docs.

Manual Verification

Added an example page use-object to the nuxt-openai example project to run and verify streaming objects works as expected.

Tasks

• 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)
• Formatting issues have been fixed (run pnpm prettier-fix in the project root)
• I have reviewed this pull request (self-review)

Related Issues

Fixes #2903

[gr2m]

Hi @tom-auger - thanks for sending your first pull request! It looks great to me!

I'm not super familiar with the UI parts of AI SDK yet, I'll reach out for a second set of eyes to make sure I'm not missing anything

[gr2m]

Great pull request Tom, thank you! Congratulations on your first contribution to the AI SDK 💐