@ai-sdk/google-vertex: Broken URL generated when using location: 'global' (Required for gemini-3.1-pro-preview) #14702

Description

When trying to use the new gemini-3.1-pro-preview model on Vertex AI, Google requires the location to be set to global. However, the SDK constructs an invalid base URL when location is set to 'global'.

The Bug: At packages/provider-utils/src/google-vertex-provider.ts (around line 272), the SDK constructs the URL like this:

typescript
https://${region}-aiplatform.googleapis.com/v1/projects/${project}/locations/${region}/publishers/google
When location: 'global' is passed, it generates: ❌ https://global-aiplatform.googleapis.com/v1/... (This host does not exist and returns ENOTFOUND).

The correct Vertex AI global endpoint does not have a region prefix: ✅ https://aiplatform.googleapis.com/v1/...

Steps to Reproduce
import { createVertex } from '@ai-sdk/google-vertex';

const vertex = createVertex({
project: 'my-project',
location: 'global', // Required for 3.1 Pro
});

const model = vertex('gemini-3.1-pro-preview');
// Throws: fetch failed -> getaddrinfo ENOTFOUND global-aiplatform.googleapis.com

Workaround
Manually overriding the baseURL bypasses the bug and successfully connects to the model:

const vertex = createVertex({
project: 'my-project',
location: 'global',
baseURL: https://aiplatform.googleapis.com/v1/projects/my-project/locations/global/publishers/google,
});

Expected Behavior
If location === 'global', the SDK should omit the ${region}- prefix from the subdomain and use aiplatform.googleapis.com.

AI SDK Version

@ai-sdk/[email protected]

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