### 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)

ERR_FAIL_COND(!is_inside_tree());
	for (int i = 0; i < gui.sub_windows.size(); i++) {
		ERR_FAIL_COND(gui.sub_windows[i].window == p_window);
	}
	if (gui.sub_windows.size() == 0) {
		subwindow_canvas = RS::get_singleton()->canvas_create();
		RS::get_singleton()->viewport_attach_canvas(viewport, subwindow_canvas);
		RS::get_singleton()->viewport_set_canvas_stacking(viewport, subwindow_canvas, SUBWINDOW_CANVAS_LAYER, 0);
	}
	SubWindow sw;
	sw.canvas_item = RS::get_singleton()->canvas_item_create();
	RS::get_singleton()->canvas_item_set_parent(sw.canvas_item, subwindow_canvas);
	sw.window = p_window;
	gui.sub_windows.push_back(sw);
	if (gui.subwindow_drag == SUB_WINDOW_DRAG_DISABLED) {
		if (p_window->get_flag(Window::FLAG_NO_FOCUS)) {
			_sub_window_update_order();
		} else {
			_sub_window_grab_focus(p_window);
		}
	} else {
		int index = _sub_window_find(gui.currently_dragged_subwindow);
		sw = gui.sub_windows[index];
		gui.sub_windows.remove_at(index);
		gui.sub_windows.push_back(sw);
		_sub_window_update_order();
	}
	RenderingServer::get_singleton()->viewport_set_parent_viewport(p_window->viewport, viewport);
}
void Viewport::_sub_window_update(Window *p_window) {