.NET: Small fixes in README - #4099

Pull request overview

Updates the .NET quickstart documentation to reflect the newer OpenAI “Responses” client API usage, aligning README examples with current SDK patterns.

Changes:

• Replace .GetOpenAIResponseClient(...) with .GetResponsesClient(...) in README code samples.
• Add using OpenAI.Responses; where needed to make Responses types/extensions available.
• Adjust .NET quickstart using blocks accordingly in both root and dotnet/ READMEs.

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 2 comments.

using System.ClientModel.Primitives;
using Azure.Identity;
using Microsoft.Agents.AI;
using OpenAI;
using OpenAI.Responses;