You may customize your own Shell using Maui Handler to disable the gesture for shell flyout.

For iOS, in Platform/iOS folder, we create a new file named CustomiOSShellHandler.cs, which implements ShellRenderer. In this class, we use the Reflection to get the PanGestureRecognizer and disable it.

public class CustomiOSShellHandler : ShellRenderer
{
    IShellFlyoutRenderer flyoutRenderer;

    protected override IShellFlyoutRenderer CreateFlyoutRenderer()
    {
        flyoutRenderer = base.CreateFlyoutRenderer();
        return flyoutRenderer;
    }

    public override void ViewWillAppear(bool animated)
    {
        base.ViewWillAppear(animated);
        var type = flyoutRenderer.GetType();
        var property = type.GetProperty("PanGestureRecognizer", System.Reflection.BindingFlags.NonPublic | System.Reflection.BindingFlags.Instance);
        var value = property.GetValue(flyoutRenderer);

        UIPanGestureRecognizer recognizer = value as UIPanGestureRecognizer;
        recognizer.Enabled = false;
    }
}

For Android, in Platform/Android folder we create a new file named CustomAndroidShellHandler which also implement ShellRenderer. Try the following code,

class CustomAndroidShellHandler: ShellRenderer
{
    protected override IShellFlyoutRenderer CreateShellFlyoutRenderer()
    {
        var flyoutRenderer = base.CreateShellFlyoutRenderer();
        flyoutRenderer.AndroidView.Touch += AndroidView_Touch;

        return flyoutRenderer;
    }

    private void AndroidView_Touch(object? sender, global::Android.Views.View.TouchEventArgs e)
    {
        if (e.Event.Action == MotionEventActions.Move)
        {
            e.Handled = true;
        }
        else
        {
            e.Handled = false;
        }
    }
}

Finally, don’t forget to add Handler in MauiProgram.cs file,

        builder.ConfigureMauiHandlers(handlers =>
        {
#if IOS
            handlers.AddHandler<Shell, CustomiOSShellHandler>();
#elif ANDROID
            handlers.AddHandler<Shell, CustomAndroidShellHandler>();
#endif
        });

For more info, you may refer to Conditional compilation.