### 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)

playing = true;
	_set_current(p_state_machine, start_request != StringName() ? start_request : p_state_machine->start_node);
	teleport_request = true;
	stop_request = false;
	start_request = StringName();
}
bool AnimationNodeStateMachinePlayback::_travel(AnimationTree *p_tree, AnimationNodeStateMachine *p_state_machine, bool p_is_allow_transition_to_self, bool p_test_only) {
	return _make_travel_path(p_tree, p_state_machine, p_is_allow_transition_to_self, path, p_test_only);
}
String AnimationNodeStateMachinePlayback::_validate_path(AnimationNodeStateMachine *p_state_machine, const String &p_path) {
	if (p_state_machine->get_state_machine_type() == AnimationNodeStateMachine::STATE_MACHINE_TYPE_GROUPED) {
		return p_path; 
	}
	String target = p_path;
	Ref<AnimationNodeStateMachine> anodesm = p_state_machine->find_node_by_path(target);
	while (anodesm.is_valid() && anodesm->get_state_machine_type() == AnimationNodeStateMachine::STATE_MACHINE_TYPE_GROUPED) {
		Vector<int> indices = anodesm->find_transition_from(anodesm->start_node);
		if (indices.size()) {
			target = target + "/" + anodesm->get_transition_to(indices[0]); 
		} else {
			break; 
		}
		anodesm = p_state_machine->find_node_by_path(target);
	}
	return target;
}
bool AnimationNodeStateMachinePlayback::_make_travel_path(AnimationTree *p_tree, AnimationNodeStateMachine *p_state_machine, bool p_is_allow_transition_to_self, Vector<StringName> &r_path, bool p_test_only) {