BackColor is an 'ambient' property. It doesn't work right because you set the labels' BackColor explicitly. Right-click the BackColor property of the labels and click Reset so it is no longer shown in bold. Changing the panel's BackColor will now automatically change the labels' BackColor as well.

This however still doesn't solve your problem. The panel's MouseLeave event will fire when you move the mouse across one of the labels. There is no clean solution for this in Winforms, subscribing all the labels and the panel's MouseEnter/Leave events doesn't eliminate corner cases. Like when the user very quickly moves the mouse from a label that's close to the edge of the panel. You'll get the MouseLeave for the label but not the MouseEnter + Leave for the panel.

The only good fix for this is a timer or the Application.Idle event. Like this:

public partial class Form1 : Form {
    public Form1() {
        InitializeComponent();
        Application.Idle += Application_Idle;
    }
    protected override void OnFormClosed(FormClosedEventArgs e) {
        Application.Idle -= Application_Idle;
        base.OnFormClosed(e);
    }
    void Application_Idle(object sender, EventArgs e) {
        var pos = panel1.PointToClient(Cursor.Position);
        if (panel1.DisplayRectangle.Contains(pos)) panel1.BackColor = Color.Red;
        else panel1.BackColor = this.BackColor;
    }
}