### Godot version

4.2

### System information

Linux

### Issue description

A nested state machine isn't traveling to its animation in `_ready()` in 4.2 as it was in 4.1.3.

In the ready function, we make the `root` state machine travel to the state of the `Stages` nested state machine. Then we immediately call the `Stages` nested state machine to travel to `Stage2`. This works fine in Godot v4.1.3, but not in Godot v4.2, where it seems a delay is first needed for the second travel animation to work.

![image](https://github.com/godotengine/godot/assets/788630/f1582a99-a68e-45d9-82b8-8367e62a9cba)
![image](https://github.com/godotengine/godot/assets/788630/c7c1f9fa-c78b-4259-bd36-81ebd8cef9aa)

### Steps to reproduce

Run the MRP below in 4.1.3 and 4.2.

In 4.1.3, the animation tree will reach `Stage2` and show Finished on the screen.

In 4.2, the animation tree will only reach `Stage1` and show Stuck on the screen.

### Minimal reproduction project

[MRP-AnimationNodeStateMachinePlayback.zip](https://github.com/godotengine/godot/files/13533132/MRP-AnimationNodeStateMachinePlayback.zip)

for (int i = 0; i < p_node->get_input_count(); i++) {
			Activity a;
			a.activity = 0;
			a.last_pass = 0;
			activity.push_back(a);
		}
		input_activity_map[p_base_path] = activity;
		input_activity_map_get[String(p_base_path).substr(0, String(p_base_path).length() - 1)] = &input_activity_map[p_base_path];
	}
	List<PropertyInfo> plist;
	p_node->get_parameter_list(&plist);
	for (PropertyInfo &pinfo : plist) {
		StringName key = pinfo.name;
		if (!property_map.has(p_base_path + key)) {
			Pair<Variant, bool> param;
			param.first = p_node->get_parameter_default_value(key);
			param.second = p_node->is_parameter_read_only(key);
			property_map[p_base_path + key] = param;
		}
		property_parent_map[p_base_path][key] = p_base_path + key;
		pinfo.name = p_base_path + key;
		properties.push_back(pinfo);
	}
	List<AnimationNode::ChildNode> children;
	p_node->get_child_nodes(&children);
	for (const AnimationNode::ChildNode &E : children) {
		_update_properties_for_node(p_base_path + E.name + "/", E.node);
	}
}
void AnimationTree::_update_properties() {