[bot] Add instrumentation for Azure.AI.Inference (Azure AI Foundry model inference)

[braintrust-bot]

Summary

The Azure.AI.Inference NuGet package (v1.0.0-beta.5, ~2.4M total downloads, updated 2025-05-14) is the official Microsoft client library for performing inference against AI models deployed through Azure AI Foundry and Azure Machine Learning Studio. It is distinct from the already-instrumented Azure.AI.OpenAI package: Azure.AI.Inference targets the Azure AI Model Inference API and supports any catalog model (LLaMA, Mistral, Phi, Cohere, etc.) via Serverless API and Managed Compute endpoints — not just OpenAI models. None of its execution surfaces are instrumented in this SDK.

Execution surfaces missing instrumentation

• Chat completions: ChatCompletionsClient.CompleteAsync — invoke any Azure AI Foundry-deployed model for chat
• Streaming chat completions: ChatCompletionsClient.CompleteStreamingAsync — streaming responses via StreamingResponse<StreamingChatCompletionsUpdate>
• Text embeddings: EmbeddingsClient.EmbedAsync — generate vector embeddings from text via the /embeddings route
• Tool/function calling: ChatCompletionsOptions.Tools — function declarations and automatic function calling within Complete/CompleteAsync
• Model info: ChatCompletionsClient.GetModelInfoAsync — retrieve deployed model metadata (name, type, provider)

Braintrust docs status

• Status: not_found — The Braintrust Azure AI Foundry integration page describes only server-side proxy configuration and has no C#/.NET SDK-level instrumentation guidance
• The Braintrust integrations directory lists Azure AI Foundry as an AI provider but with no Azure.AI.Inference-specific instrumentation
• No C#-specific Azure.AI.Inference instrumentation is referenced anywhere in Braintrust docs

Upstream sources

• NuGet: https://www.nuget.org/packages/Azure.AI.Inference (v1.0.0-beta.5)
• Official docs / README: https://learn.microsoft.com/en-us/dotnet/api/overview/azure/ai.inference-readme
• API reference: https://learn.microsoft.com/en-us/dotnet/api/azure.ai.inference
• GitHub source: https://github.com/Azure/azure-sdk-for-net/tree/main/sdk/ai/Azure.AI.Inference
• Azure AI Model Inference API: https://learn.microsoft.com/en-us/azure/ai-studio/reference/reference-model-inference-api

Local repo files inspected

• src/Braintrust.Sdk.OpenAI/ — instruments OpenAI SDK only
• src/Braintrust.Sdk.AzureOpenAI/ — instruments Azure.AI.OpenAI only (different package and API surface)
• src/Braintrust.Sdk.Anthropic/ — instruments Anthropic SDK only
• src/Braintrust.Sdk.AgentFramework/ — instruments Microsoft.Extensions.AI.IChatClient middleware only
• Grep for Azure.AI.Inference, ChatCompletionsClient, and EmbeddingsClient across the entire repo returned zero results