### 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)

} else {
			gui.subwindow_focused = nullptr;
		}
	}
	RenderingServer::get_singleton()->viewport_set_parent_viewport(p_window->viewport, p_window->parent ? p_window->parent->viewport : RID());
}
int Viewport::_sub_window_find(Window *p_window) const {
	for (int i = 0; i < gui.sub_windows.size(); i++) {
		if (gui.sub_windows[i].window == p_window) {
			return i;
		}
	}
	return -1;
}
void Viewport::_update_viewport_path() {
	if (viewport_textures.is_empty()) {
		return;
	}
	Node *scene_root = get_scene_file_path().is_empty() ? get_owner() : this;
	if (!scene_root && is_inside_tree()) {
		scene_root = get_tree()->get_edited_scene_root();
	}
	if (scene_root && (scene_root == this || scene_root->is_ancestor_of(this))) {
		NodePath path_in_scene = scene_root->get_path_to(this);
		for (ViewportTexture *E : viewport_textures) {
			E->path = path_in_scene;
		}
	}
}
void Viewport::_notification(int p_what) {