Invoke API of another application which has form authentication

As you mentioned in the comments you have to make a C# HTTP call to the other project Web API. You can do it by creating anywhere in your project a class named MakeRequestService and one static method named MakeWebRequest, which will return a string, being the JSON you need.

public class MakeRequestService
{
    public static string MakeWebRequest(string url, string verb, int timeout, Dictionary<string, string> headers = null, string contentType = "", string json = "")
    {
        string myResult = string.Empty;
    
        try
        {
            HttpWebRequest myRequest = (HttpWebRequest)WebRequest.Create(url);
            myRequest.Method = verb;
            myRequest.Timeout = timeout;
    
            if (!string.IsNullOrEmpty(contentType))
                myRequest.ContentType = contentType;
    
            if (headers != null)
            {
                foreach (var header in headers)
                {
                    if (header.Key == HttpRequestHeader.Accept.ToString())
                        myRequest.Accept = header.Value;
                    else
                        myRequest.Headers.Add(header.Key, header.Value);
                }
            }
    
            if (!string.IsNullOrEmpty(json))
            {
                byte[] bytes = Encoding.UTF8.GetBytes(json);
                myRequest.ContentLength = bytes.Length;
    
                using (var streamWriter = new StreamWriter(myRequest.GetRequestStream()))
                {
                    streamWriter.Write(json);
                    streamWriter.Flush();
                    streamWriter.Close();
                }
            }
    
            using (HttpWebResponse response = myRequest.GetResponse() as HttpWebResponse)
            {
                StreamReader reader = new StreamReader(response.GetResponseStream());
                myResult = reader.ReadToEnd();
            }
        }
        catch (WebException ex)
        {
            if (ex.Status == WebExceptionStatus.ProtocolError)
            {
                if (ex.Response is HttpWebResponse response)
                {                
                    Stream stream = response.GetResponseStream();
                    StreamReader sr = new StreamReader(stream: stream);
                    myResult = sr.ReadToEnd();
                    stream.Position = 0;                
                }
            }
            else
            {
                myResult = ex.Message;
            }
        }
    
        return myResult;
    }
}

You can then use this method in the following way:

string res = MakeRequestService.MakeWebRequest(
    url: "The FULL URL of the first project, based on your example, e.g. http://localhost:69963/api/customer",
    verb: "POST",
    contentType: "application/json"
    );

var outcome = JsonConvert.DeserializeObject<IEnumerable<Customer>>(res);

The catch block in the MakeWebRequest method is just an example and will return a plain string containing the JSON error body in case of an unsuccessful API call. You can modify it for your needs, e.g. rethrow the WebException and handle it the way you want.

The MakeWebRequest method is very abstract so you can use it for the API calls as well. If you make a POST request with JSON body - just pass the body to the json parameter. If you make a GET request with query parameters, just build the whole URL, containing the query parameters, and then invoke the method.

Here is some code I use to login with a C# app. You will need to modify to work with your application. The SharedCookie will need to be added to each future request since it has your Session Cookie included.

    public void Login()
    {
        byte[] bytes;
        string data;
        SharedCookie = new CookieContainer();

        var url = Host + "/login";
        
        try
        {
            //Start Session
            var request = CreateRequest(url, "GET");
            request.CookieContainer = SharedCookie;

            using (var tmpResponse = request.GetResponse())
            {
                DoWriteResponse(tmpResponse);
                tmpResponse.Close();
            }

            //Login
            
            data = "username=user&password=pass";
            bytes = Encoding.UTF8.GetBytes(data);

            request = CreateRequest(url, "POST");
            request.CookieContainer = SharedCookie;

            using (var stream = request.GetRequestStream())
            {
                stream.Write(bytes, 0, bytes.Length);
            }

            using (var tmpResponse = request.GetResponse())
            {
                DoWriteResponse(tmpResponse);
                tmpResponse.Close();
            }
            IsLoggedIn = true;
        }
        catch (System.Net.WebException ex)
        {
            Console.WriteLine("Web Error:" + ex.Status);
            Console.WriteLine("Url:" + url);
            Console.WriteLine(ex.Message);
        }
        catch (Exception ex)
        {
            Console.WriteLine("Url:" + url);
            Console.WriteLine(ex.Message);
        }
    }

    private void DoWriteResponse(WebResponse tmpResponse)
    {
        if (debug)
        {
            Console.WriteLine("************BEGIN**************");
            Console.WriteLine("************" + tmpResponse.ResponseUri + "**************");
            Console.WriteLine("*******************************");
            using (var reader = new StreamReader(tmpResponse.GetResponseStream()))
            {
                var pageText = reader.ReadToEnd();
                Console.WriteLine(pageText);
            }
            Console.WriteLine("*************END***************");
        }
    }

    private HttpWebRequest CreateRequest(string url, string method)
    {
        var request = (HttpWebRequest)WebRequest.Create(url);
        request.Referer = Host;
        request.UserAgent = "Mozilla/5.0 (Windows NT 6.1; WOW64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/35.0.1916.153 Safari/537.36";
        request.Method = method;
        request.ContentType = "application/x-www-form-urlencoded; charset=UTF-8";

        return request;
    }