One option if you're really struggling, would be to create a small little application that is configured to run at startup that creates a notification tray icon.

If you download Visual Studio 2019 Community version, you could create a new C# .Net Forms application with the following code:
using System;
using System.Collections.Generic;
using System.Linq;
using System.Windows.Forms;
using System.Globalization;
namespace WeekCounter
{
static class Program
{
[STAThread]
static void Main()
{
Application.EnableVisualStyles();
Application.SetCompatibleTextRenderingDefault(false);
Application.Run(new MyCustomApplicationContext());
}
private static void MessageBox(string v)
{
throw new NotImplementedException();
}
}
public class MyCustomApplicationContext : ApplicationContext
{
private NotifyIcon trayIcon;
public MyCustomApplicationContext()
{
// Initialize Tray Icon
trayIcon = new NotifyIcon()
{
Icon = WeekCounter.Properties.Resources.icon,
Text = "WeekCounter",
ContextMenu = new ContextMenu(new MenuItem[] {
new MenuItem("Exit", Exit)
}),
Visible = true
};
trayIcon.MouseMove += new MouseEventHandler(notifyIcon1_MouseMove);
}
private void notifyIcon1_MouseMove(object sender, MouseEventArgs e)
{
CultureInfo myCI = new CultureInfo("en-US");
Calendar myCal = myCI.Calendar;
CalendarWeekRule myCWR = myCI.DateTimeFormat.CalendarWeekRule;
DayOfWeek myFirstDOW = myCI.DateTimeFormat.FirstDayOfWeek;
trayIcon.Text = "Time: " + DateTime.Now.ToString("MM/dd/yyyy h:mm:ss tt") + "\nWeek: " + myCal.GetWeekOfYear(DateTime.Now, myCWR, myFirstDOW);
}
void Exit(object sender, EventArgs e)
{
trayIcon.Visible = false;
Application.Exit();
}
}
}
Note: Under the "Resources" for the project you can add a suitable ico file as an icon resource. It is referenced in the code as "icon" so the resource will need to be named that:
Icon = WeekCounter.Properties.Resources.icon

You could ensure the exe is run at startup by adding a reference to it under the registry key:
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Run