Add streaming support with IAsyncEnumerable

[GmausDev]

Summary

Add streaming response support using IAsyncEnumerable<T> for chat completions, enabling real-time token-by-token output similar to other AI SDKs.

Current Behavior

All responses are returned only after the complete response is received:

var response = await client.ChatAsync("Tell me a story");
Console.WriteLine(response); // Only prints after full response

Proposed API

// New streaming method
await foreach (var chunk in client.ChatStreamAsync("Tell me a story"))
{
    Console.Write(chunk.Delta?.Content); // Print tokens as they arrive
}

// Or with the full request object
var request = new ChatCompletionRequest 
{ 
    Stream = true,
    Messages = [...] 
};
await foreach (var chunk in client.CreateChatCompletionStreamAsync(request))
{
    // Process each chunk
}

Implementation Details

New Types Needed

public class ChatCompletionChunk
{
    public string Id { get; set; }
    public List<ChatChunkChoice> Choices { get; set; }
}

public class ChatChunkChoice
{
    public int Index { get; set; }
    public ChatChunkDelta Delta { get; set; }
    public string? FinishReason { get; set; }
}

public class ChatChunkDelta
{
    public string? Role { get; set; }
    public string? Content { get; set; }
}

SSE Parsing

Parse Server-Sent Events (SSE) format:

data: {"id":"...","choices":[{"delta":{"content":"Hello"}}]}

data: {"id":"...","choices":[{"delta":{"content":" world"}}]}

data: [DONE]

Expected Benefits

• Real-time output - Display tokens as they're generated
• Better UX - Users see immediate feedback
• Lower perceived latency - First token appears faster
• Feature parity - Match capabilities of other AI SDKs

Priority

🟡 P1 - High Impact

Dependencies

• Use HttpCompletionOption.ResponseHeadersRead for faster response start #2 (HttpCompletionOption.ResponseHeadersRead) should be implemented first