RestSharp.TwitterClient.cs

using System.Text.Json.Serialization;
using RestSharp.Authenticators;

namespace RestSharp.Tests.External.Twitter;

public interface ITwitterClient {
    Task<TwitterUser> GetUser(string user);
}

public class TwitterClient : ITwitterClient, IDisposable {
    readonly RestClient _client;

    public TwitterClient(string apiKey, string apiKeySecret) {
        var options = new RestClientOptions("https://api.twitter.com/2");

        _client = new RestClient(options) {
            Authenticator = new TwitterAuthenticator("https://api.twitter.com", apiKey, apiKeySecret)
        };
    }

    public async Task<TwitterUser> GetUser(string user) {
        var response = await _client.GetJsonAsync<TwitterSingleObject<TwitterUser>>(
            "users/by/username/{user}",
            new { user }
        );
        return response!.Data;
    }

    record TwitterSingleObject<T>(T Data);

    public void Dispose() {
        _client?.Dispose();
        GC.SuppressFinalize(this);
    }
}

public class TwitterAuthenticator : AuthenticatorBase {
    readonly string _baseUrl;
    readonly string _clientId;
    readonly string _clientSecret;

    public TwitterAuthenticator(string baseUrl, string clientId, string clientSecret) : base("") {
        _baseUrl      = baseUrl;
        _clientId     = clientId;
        _clientSecret = clientSecret;
    }

    protected override async ValueTask<Parameter> GetAuthenticationParameter(string accessToken) {
        var token = string.IsNullOrEmpty(Token) ? await GetToken() : Token;
        return new HeaderParameter(KnownHeaders.Authorization, token);
    }

    async Task<string> GetToken() {
        var options = new RestClientOptions(_baseUrl);

        using var client = new RestClient(options) {
            Authenticator = new HttpBasicAuthenticator(_clientId, _clientSecret),
        };

        var request = new RestRequest("oauth2/token")
            .AddParameter("grant_type", "client_credentials");
        var response = await client.PostAsync<TokenResponse>(request);
        return $"{response!.TokenType} {response!.AccessToken}";
    }

    record TokenResponse {
        [JsonPropertyName("token_type")]
        public string TokenType { get; init; }
        [JsonPropertyName("access_token")]
        public string AccessToken { get; init; }
    }
}

public record TwitterUser(string Id, string Name, string Username);

@keyse just inform during the creation of the RestClientOptions instance:

 async Task<TokenResponse> GetToken() 
{
        //here
       var options = new RestClientOptions(_baseUrl){ Authenticator = new HttpBasicAuthenticator(_clientId, _clientSecret) };
        //not here
        using var client = new RestClient(options) { // Authenticator = new HttpBasicAuthenticator(_clientId, _clientSecret) };

        var request = new RestRequest("oauth2/token") .AddParameter("grant_type", "client_credentials");

        return await client.PostAsync<TokenResponse>(request); 
} 

@alexeyzimarev thanks for your example, it was a great help!