Update vertex ai provider docs with api key info (#2519)

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## Issue Reference
Please link to any related issues
- [ ] This PR fixes/closes #[issue number]

## Changes
This PR adds documentation for using Vertex AI API Keys (Express Mode)
to the Vertex AI provider docs. This aims to simplify the initial setup
for users by recommending a faster alternative to service account
authentication.

The changes include:
- A new section detailing how to configure a Vertex AI client with an
API key using `query_params`.
- An `Info` note recommending Express Mode for quick starts and linking
to Google's official guide.
- Clarification on explicitly setting `project_id` and omitting
`credentials` when using an API key.
- An updated `ParamField` for `query_params` to include the API key
example.

## Testing
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- [ ] Unit tests added/updated
- [X] Manual testing performed (verified documentation renders
correctly)
- [ ] Tested in [environment]

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## PR Checklist
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- [X] I have read and followed the contributing guidelines
- [X] My code follows the style guidelines of this project
- [X] I have performed a self-review of my own code
- [X] I have commented my code, particularly in hard-to-understand areas
- [X] I have made corresponding changes to the documentation
- [X] My changes generate no new warnings

## Additional Notes
This change directly addresses the user request to document the Vertex
API Key (Express Mode) for faster onboarding, including a recommendation
and a link to the official Google documentation.

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Author: aaronvg

fern/03-reference/baml/clients/providers/vertex.mdx

@@ -45,6 +45,35 @@ can expect authentication to work out of the box.
 Setting [`options.credentials`](#credentials) will take precedence and force `vertex-ai` to load
 service account credentials from that file path.
 
+### Using a Vertex API Key (Express Mode)
+
+<Info>
+  To get started quickly, we recommend using Express Mode with a Vertex API Key.
+  This avoids service account setup and works well for prototyping.
+
+  See Google's guide: [Use Vertex API keys (Express Mode)](https://cloud.google.com/vertex-ai/generative-ai/docs/start/api-keys?usertype=expressmode).
+</Info>
+
+When using a Vertex API Key, set the `key` query parameter and specify your `project_id` and `location`:
+
+```baml BAML
+client<llm> VertexApiKeyClient {
+  provider vertex-ai
+  options {
+    model gemini-2.5-pro
+    location us-central1
+    project_id my-project-id
+    query_params {
+      key env.VERTEX_API_KEY
+    }
+  }
+}
+```
+
+Notes:
+- `project_id` cannot be inferred when using an API key; set it explicitly.
+- Keep `credentials` unset when using an API key, so BAML does not prefer service account auth.
+
 ### Playground
 To use a `vertex-ai` client in the playground, all you need to do is run `gcloud
 auth application-default login` in the terminal. The playground will then use these
@@ -334,6 +363,27 @@ client<llm> MyClient {
 ```
 </ParamField>
 
+<ParamField path="query_params" type="object">
+  Query string parameters appended to the request URL.
+
+Example (use a Vertex API Key with Express Mode):
+```baml BAML
+client<llm> MyClient {
+  provider vertex-ai
+  options {
+    model gemini-2.5-pro
+    project_id my-project-id
+    location us-central1
+    query_params {
+      key env.VERTEX_API_KEY
+    }
+  }
+}
+```
+
+  When using an API key, omit `credentials` and set `project_id` explicitly.
+</ParamField>
+
 <Markdown src="/snippets/role-selection.mdx" />
 
 <Markdown src="/snippets/allowed-role-metadata-basic.mdx" />