### 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)

Rect2 swrect = Rect2i(sw->get_position(), sw->get_size());
					if (!sw->get_flag(Window::FLAG_BORDERLESS)) {
						int title_height = sw->get_theme_constant(SNAME("title_height"));
						swrect.position.y -= title_height;
						swrect.size.y += title_height;
					}
					if (swrect.has_point(viewport_pos)) {
						viewport_under = sw;
						viewport_pos -= sw->get_position();
					}
				}
				if (!viewport_under) {
					
					viewport_under = embedder;
				}
			} else {
				
				Vector2i screen_mouse_pos = DisplayServer::get_singleton()->mouse_get_position();
				DisplayServer::WindowID window_id = DisplayServer::get_singleton()->get_window_at_screen_position(screen_mouse_pos);
				if (window_id != DisplayServer::INVALID_WINDOW_ID) {
					ObjectID object_under = DisplayServer::get_singleton()->window_get_attached_instance_id(window_id);
					if (object_under != ObjectID()) { 
						Window *w = Object::cast_to<Window>(ObjectDB::get_instance(object_under));
						if (w) {
							viewport_under = w;
							viewport_pos = screen_mouse_pos - w->get_position();
						}
					}
				}
			}