### Godot version

v4.1.stable.official [970459615]

### System information

Godot v4.1.stable - Windows 10.0.22621 - Vulkan (Forward+) - dedicated NVIDIA GeForce GTX 1660 Ti (NVIDIA; 31.0.15.3598) - AMD Ryzen 7 3700X 8-Core Processor (16 Threads)

### Issue description

is_input_handled() is returning True, even though set_input_as_handled() has not been called.

Example:
`func _input_event(viewport, event, shape_idx):
	print(viewport.is_input_handled())`

Returns 'True', should return 'False'

### Steps to reproduce

1. Create a new project and add a Node2D as the root
2. Add a child Area2D node containing a CollisionShape2D and a Sprite2D
3. Either create the _input_event(viewport, event, shape_idx) or connect _on_input_event(viewport, event, shape_idx)
4. Print viewport.is_input_handled()
5. True is printed.

### Minimal reproduction project

[input_test.zip](https://github.com/godotengine/godot/files/12063748/input_test.zip)

} break;
		case NOTIFICATION_VP_MOUSE_EXIT: {
			gui.mouse_in_viewport = false;
			_drop_physics_mouseover();
			_drop_mouse_over();
			_gui_cancel_tooltip();
			
			
			
		} break;
		case NOTIFICATION_WM_WINDOW_FOCUS_OUT: {
			_gui_cancel_tooltip();
			_drop_physics_mouseover();
			if (gui.mouse_focus && !gui.forced_mouse_focus) {
				_drop_mouse_focus();
			}
			
			
			
			
		} break;
		case NOTIFICATION_PREDELETE: {
			if (gui_parent) {
				gui_parent->gui.tooltip_popup = nullptr;
				gui_parent->gui.tooltip_label = nullptr;
			}
		} break;
	}
}
void Viewport::_process_picking() {