.Net: feat: Add support for dimensions in Vertex AI embedding services

[abbottdev]

Motivation and Context

Why is this change required?
PR #10489 added support for configuring embedding [dimensions] (outputDimensionality) for the Google AI connector, but the equivalent Vertex AI connector was not updated. This means specifying [Dimensions] in [EmbeddingGenerationOptions] or via the constructor has no effect when using Vertex AI — the API always returns the model's default dimensionality.

What problem does it solve?
When using [VertexAIEmbeddingGenerator] or [VertexAITextEmbeddingGenerationService]with a [dimensions] value (e.g. 128), the output embedding length is the model default (e.g. 3072) instead of the requested size.

What scenario does it contribute to?
Users who need to control embedding dimensionality for storage optimization, performance, or compatibility with downstream systems when using the Vertex AI endpoint.

Fixes: #12988

Description

This PR adds outputDimensionality support to the Vertex AI embedding connector, mirroring the existing Google AI implementation from PR #10489.

The Google connector has two parallel embedding paths — Google AI (uses API key, calls generativelanguage.googleapis.com) and Vertex AI (uses bearer token, calls [{location}-aiplatform.googleapis.com]). PR #10489 only wired up dimensions for the Google AI path. This PR applies the same pattern to every layer of the Vertex AI path.

The key structural difference between the two APIs is where outputDimensionality goes in the request JSON:

Google AI puts it per-content-item: { "requests": [{ "content": {...}, "outputDimensionality": 128 }] }
Vertex AI puts it in the shared parameters block: { "instances": [...], "parameters": { "autoTruncate": false, "outputDimensionality": 128 } }
The implementation follows this difference. In [VertexAIEmbeddingRequest], outputDimensionality is added to the existing [RequestParameters] class (alongside autoTruncate), rather than on each instance item.

Dimensions flow through the same chain as Google AI:

1. Extension methods accept int? dimensions = null and pass it to the generator/service constructor
2. [VertexAIEmbeddingGenerator] passes it to [VertexAITextEmbeddingGenerationService]
3. The service passes it to [VertexAIEmbeddingClient], which stores it as a default
4. At request time, the client resolves the final value as [options?.Dimensions ?? this._dimensions] — runtime [EmbeddingGenerationOptions] take priority over the constructor default
5. [VertexAIEmbeddingRequest.FromData()] sets it on the parameters block, and [JsonIgnore(WhenWritingNull)] ensures it's omitted when not specified

All new parameters default to null, preserving full backward compatibility.

Contribution Checklist

• The code builds clean without any errors or warnings
• The PR follows the SK Contribution Guidelines and the pre-submission formatting script raises no violations
• All unit tests pass, and I have added new tests where possible
• I didn't break anyone 😄