Session-based singleton service in ASP.NET Core MVC

I'm building a ASP.NET MVC page as a webclient for my own application.
My application provides a "ClientConnector" handling all requests to the server and handling authentication ...

For the WPF client there is no problem - I create a new instance of the ClientConnector when I start the client and all is fine.

But when using the webclient I need to create the instance for every browser session - but within the session the instance needs to be consistent.

I found a few information about session handling and session variables - but all the examples only work with simple values but not with complex objects.

May anybody provide a simple (and complete) example for implementing this idea?

Currently I added the "new"-command within the "ConfigureServices" method in the startup.cs.

services.AddSingleton(new ClientConnector());

But of course this way the ClientConnector is persistent for the complete application - independent of the browser session.

Thanks and regards

Markus

Thanks for the idea @Timofeus:

I created a simple dictionary as the service - storing a session id and the actual client connector.

Then I added the following code to a base controller class where my actual controller inherits from, just to make everything a little more clean.
(here all the code, if somebody comes over this post)

ClientConnectors.cs

public class ClientConnectors
{
  private readonly Dictionary<string, ClientConnector> _clients;
  
  public ClientConnectors()
  {
    _clients = new Dictionary<string, ClientConnector>();
  }

  public ClientConnector GetClientConnectorForSession(string sessionId)
  {
    if (_clients.ContainsKey(sessionId))
    {
      return _clients[sessionId];
    }
    else
    {
      var client = new ClientConnector();
      _clients.Add(sessionId, client);
       return client;
    }
  }
}

BaseController.cs

public class BaseController : Controller
    {
        protected readonly ILogger<HomeController> _logger;
        protected ClientConnector _client;
    private ClientConnectors _clients;
    private IHttpContextAccessor _httpContextAccessor;

        public BaseController(ILogger<HomeController> logger, ClientConnectors clients, IHttpContextAccessor httpContextAccessor)
    {
        _logger = logger;
        _clients = clients;
        _httpContextAccessor = httpContextAccessor;
        IdentifyClientConnection();
    }

        private void IdentifyClientConnection()
        {
            _client = _clients.GetClientConnectorForSession(CreateOrGetSessionId());
        }

        private string CreateOrGetSessionId()
    {
        var returnValue = _httpContextAccessor.HttpContext.Session.GetString("MoxSessionId");
        
        if (string.IsNullOrEmpty(returnValue))
        {
            returnValue = Guid.NewGuid().ToString();
            _httpContextAccessor.HttpContext.Session.SetString("MoxSessionId", returnValue);
        }
        
        return returnValue;
    }
    }

HomeController.cs

public class HomeController : BaseController
    {
        public HomeController(ILogger<HomeController> logger, ClientConnectors clients, IHttpContextAccessor hca) : base(logger, clients, hca) { }

        public IActionResult Index()
        {
            var model = new HomeViewModel(_client.IncreaseAndDisplayCounter());
            return View(model);
        }
    }