V4 (docs): add Vercel AI SDK integration with browser-ai/transformers-js package

[jakobhoeg]

Replaces #1514: rebased onto v4 as requested. @nico-martin

This PR proposes adding documentation for using Transformers.js with the Vercel AI SDK via the @browser-ai/transformers-js community model provider. This is an idea/suggestion for the core docs, happy to adjust or remove if you feel like it doesn't fit.

Closes #1389

Summary
Adds a developer guide (docs/source/guides/vercel-ai-sdk.md) covering usage of Transformers.js as a Vercel AI SDK model provider via @browser-ai/transformers-js npm package. Text generation, embeddings, vision, transcription, tool calling, Web Workers, download progress, useChat transport, and browser fallback.
Adds a step-by-step tutorial (docs/source/tutorials/next-ai-sdk.md) for building a Next.js AI chatbot from scratch with WebGPU, tool calling, and human-in-the-loop approval.

[jakobhoeg]

@nico-martin let me know what you think :)

[nico-martin]

Hi @jakobhoeg, I'm really sorry it took me so long to answer. We were quite busy with demos based on v4 and some issues, but I'm looking at it right now :)

[jakobhoeg]

Hi @nico-martin,
No worries at all! Thank you for taking a look :)

[nico-martin]

Right now the Build PR Documentation workflow fails. I think you need to add the new files to the Table of contents: packages/transformers/docs/source/_toctree.yml

1. Tutorial — Next.js AI Chatbot (under "Tutorials")

- local: tutorials/next-ai-sdk
  title: Building a Next.js AI Chatbot with Vercel AI SDK

Add this as the last item in the Tutorials section (after tutorials/node).

2. Developer Guide — Vercel AI SDK (under "Developer Guides")

- local: guides/vercel-ai-sdk
  title: Using Transformers.js with the Vercel AI SDK

Add this as the last item in the Developer Guides section (after guides/node-audio-processing).

[jakobhoeg]

Hi @nico-martin,
Thanks for the review! Your availability request is unfortunately not feasible to resolve atm.
I resolved the other ones. Let me know if there's anything else you need from me :)

EDIT: After reviewing the doc link below, I've also pushed some minor refinements that have changed since opening the PR.

[HuggingFaceDocBuilderDev]

The docs for this PR live here. All of your documentation changes will be reflected on that endpoint. The docs are available until 30 days after the last update.

[jakobhoeg]

@nico-martin pushed some minor adjustments