docs: add Synthorai to the OpenAI-compatible providers documentation (#19678)

## Background

The OpenAI-compatible providers documentation omitted Synthorai despite
its verified Chat Completions endpoint and compatibility with the
package-free integration pattern.

## Summary

Added a Synthorai provider page with installation, configuration, model
selection, generation, and streaming examples, and linked it from the
OpenAI-compatible providers index.

## Testing

Passed pnpm check, pnpm validate:docs, pnpm type-check:full, and a
mocked generateText runtime probe. The initial root-level probe could
not resolve the workspace package and was rerun successfully from the
ai-functions example workspace.

## Related Issues

Fixes #19675

Co-authored-by: ai-sdk-factory <308175966+ai-sdk-factory@users.noreply.github.com>
Co-authored-by: cuihuan <4251372+cuihuan@users.noreply.github.com>