How to update progress bar from other class?

Create a public property or a public method in the form containing the progress bar

public void SetProgress(int progress)
{
    progressBar.Progress = progress;
}

Now you can update the progress bar with

myForm.SetProgress(50);

---

Another approach is to have a ProgressChanged event somewhere and let the form subscribe to this event.

public class Tool {
    public event Action<int> ProgressChanged;

    private void OnProgressChanged(int progress) 
    {
        var eh = ProgressChanged;
        if (eh != null) {
            eh(progress);
        }
    }

    public void DoSomething()
    {
        ...
        OnProgressChanged(30);
        ...
    }
}

In the form you would have something like this

private Tool _tool;

public MyForm () // Constructor of your form
{
    _tool = new Tool();
    _tool.ProgressChanged += Tool_ProgressChanged;
}

private void Tool_ProgressChanged(int progress)
{
    progressBar.Progress = progress;
}