### 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)

} else if (prop_name == "graph_offset") {
		r_ret = get_graph_offset();
		return true;
	}
	return false;
}
void AnimationNodeStateMachine::_get_property_list(List<PropertyInfo> *p_list) const {
	List<StringName> names;
	for (const KeyValue<StringName, State> &E : states) {
		names.push_back(E.key);
	}
	names.sort_custom<StringName::AlphCompare>();
	for (const StringName &prop_name : names) {
		p_list->push_back(PropertyInfo(Variant::OBJECT, "states/" + prop_name + "/node", PROPERTY_HINT_RESOURCE_TYPE, "AnimationNode", PROPERTY_USAGE_NO_EDITOR));
		p_list->push_back(PropertyInfo(Variant::VECTOR2, "states/" + prop_name + "/position", PROPERTY_HINT_NONE, "", PROPERTY_USAGE_NO_EDITOR));
	}
	p_list->push_back(PropertyInfo(Variant::ARRAY, "transitions", PROPERTY_HINT_NONE, "", PROPERTY_USAGE_NO_EDITOR));
	p_list->push_back(PropertyInfo(Variant::VECTOR2, "graph_offset", PROPERTY_HINT_NONE, "", PROPERTY_USAGE_NO_EDITOR));
	for (PropertyInfo &E : *p_list) {
		_validate_property(E);
	}
}
void AnimationNodeStateMachine::_validate_property(PropertyInfo &p_property) const {
	if (p_property.name == "allow_transition_to_self" || p_property.name == "reset_ends") {
		if (state_machine_type == STATE_MACHINE_TYPE_GROUPED) {
			p_property.usage = PROPERTY_USAGE_NONE;
		}
	}
}
void AnimationNodeStateMachine::reset_state() {