Add JsonPatch support for Chat, Responses, and Embeddings

examples/Responses/Example09_ModelOverridePerRequest.cs

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+using NUnit.Framework;
+using OpenAI.Responses;
+using System;
+
+namespace OpenAI.Examples;
+
+// This example uses experimental APIs which are subject to change. To use experimental APIs,
+// please acknowledge their experimental status by suppressing the corresponding warning.
+#pragma warning disable OPENAI001
+#pragma warning disable SCME0001 // Type is for evaluation purposes only and is subject to change or removal in future updates.
+
+public partial class ResponseExamples
+{
+    [Test]
+    public void Example09_ModelOverridePerRequest()
+    {
+        OpenAIResponseClient client = new(model: "gpt-4o", apiKey: Environment.GetEnvironmentVariable("OPENAI_API_KEY"));
+
+        // Add extra request fields using Patch.
+        // Patch lets you set fields like `model` that aren't exposed on ResponseCreationOptions.
+        // See the API docs https://platform.openai.com/docs/api-reference/responses/create for supported additional fields.
+        ResponseCreationOptions options = new();
+        options.Patch.Set("$.model"u8, "gpt-5");
+
+        OpenAIResponse response = client.CreateResponse("Say 'this is a test.", options);
+
+        Console.WriteLine($"[ASSISTANT]: {response.GetOutputText()}, [Mode]: {response.Model}");
+    }
+}
+
+#pragma warning disable SCME0001 // Type is for evaluation purposes only and is subject to change or removal in future updates.
+#pragma warning restore OPENAI001

examples/Responses/Example09_ModelOverridePerRequestAsync.cs

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+using NUnit.Framework;
+using OpenAI.Responses;
+using System;
+using System.Threading.Tasks;
+
+namespace OpenAI.Examples;
+
+// This example uses experimental APIs which are subject to change. To use experimental APIs,
+// please acknowledge their experimental status by suppressing the corresponding warning.
+#pragma warning disable OPENAI001
+#pragma warning disable SCME0001 // Type is for evaluation purposes only and is subject to change or removal in future updates.
+
+public partial class ResponseExamples
+{
+    [Test]
+    public async Task Example09_ModelOverridePerRequestAsync()
+    {
+        OpenAIResponseClient client = new(model: "gpt-4o", apiKey: Environment.GetEnvironmentVariable("OPENAI_API_KEY"));
+
+        // Add extra request fields using Patch.
+        // Patch lets you set fields like `model` that aren't exposed on ResponseCreationOptions.
+        // See the API docs https://platform.openai.com/docs/api-reference/responses/create for supported additional fields.
+        ResponseCreationOptions options = new();
+        options.Patch.Set("$.model"u8, "gpt-5");
+
+        OpenAIResponse response = await client.CreateResponseAsync("Say 'this is a test.", options);
+
+        Console.WriteLine($"[ASSISTANT]: {response.GetOutputText()}, [Mode]: {response.Model}");
+    }
+}
+
+#pragma warning disable SCME0001 // Type is for evaluation purposes only and is subject to change or removal in future updates.
+#pragma warning restore OPENAI001