formato.cs

using Newtonsoft.Json;

namespace ConsoleApp1
{
    internal class Program
    {
        static void Main(string[] args)
        {
            var message = new Message
            {
                Role = "user",
                Content = "What is the Microsoft mission"
            };

            var message2 = new Message
            {
                Role = "bot",
                Content = "Empower every person and every organization on the planet to achieve more."
            };

            var messageList = new MessageList
            {
                Messages = new List<Message> { message, message2 }
            };

            var json = JsonConvert.SerializeObject(messageList, new JsonSerializerSettings { ContractResolver = new CamelCasePropertyNamesContractResolver() });
            Console.WriteLine(json);
        }
    }

    public class Message
    {
        public string Role { get; set; }
        public string Content { get; set; }
    }

    public class MessageList
    {
        public List<Message> Messages { get; set; }
    }


    // "messages": [{"role": "user", "content": "What is the Microsoft mission"}]
}

using Newtonsoft.Json;
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Xml;

namespace ConsoleEliminame
{
public class MiClase
{
[JsonProperty("messages")]
public Message[] Messages { get; set; }
}

public class Message
{
    [JsonProperty("role")]
    public string Role { get; set; }

    [JsonProperty("content")]
    public string Content { get; set; }
}

internal class Program
{
    static void Main(string[] args)
    {
        var miClase = new MiClase
        {
            Messages = new Message[]
            {
                new Message { Role = "Message1", Content = "What is the Microsoft mission" },
                new Message { Role = "Message2", Content = "What is the Google" },
                new Message { Role = "Message3", Content = "What is the Linux" }
            }
        };

        string json = JsonConvert.SerializeObject(miClase, Newtonsoft.Json.Formatting.Indented);
        Console.WriteLine(json);
    }
}

}

using Newtonsoft.Json; using System; using System.Collections.Generic; using System.Linq; using System.Text; using System.Threading.Tasks; using System.Xml;

namespace ConsoleEliminame { public class MiClase { [JsonProperty("messages")] public Message[] Messages { get; set; } }

public class Message
{
    [JsonProperty("role")]
    public string Role { get; set; }

    [JsonProperty("content")]
    public string Content { get; set; }
}

internal class Program
{
    static void Main(string[] args)
    {
        var miClase = new MiClase
        {
            Messages = new Message[]
            {
                new Message { Role = "Message1", Content = "What is the Microsoft mission" },
                new Message { Role = "Message2", Content = "What is the Google" },
                new Message { Role = "Message3", Content = "What is the Linux" }
            }
        };

        string json = JsonConvert.SerializeObject(miClase, Newtonsoft.Json.Formatting.Indented);
        Console.WriteLine(json);
    }
}

}

Instead of using attributes on any property to get lowercase properties I use a ContractResolver, looks more clean for me.