### 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)

BIND_ENUM_CONSTANT(ADVANCE_MODE_ENABLED);
	BIND_ENUM_CONSTANT(ADVANCE_MODE_AUTO);
	ADD_SIGNAL(MethodInfo("advance_condition_changed"));
}
AnimationNodeStateMachineTransition::AnimationNodeStateMachineTransition() {
}
void AnimationNodeStateMachinePlayback::_set_current(AnimationNodeStateMachine *p_state_machine, const StringName &p_state) {
	current = p_state;
	if (current == StringName()) {
		group_start_transition = Ref<AnimationNodeStateMachineTransition>();
		group_end_transition = Ref<AnimationNodeStateMachineTransition>();
		return;
	}
	Ref<AnimationNodeStateMachine> anodesm = p_state_machine->find_node_by_path(current);
	if (!anodesm.is_valid()) {
		group_start_transition = Ref<AnimationNodeStateMachineTransition>();
		group_end_transition = Ref<AnimationNodeStateMachineTransition>();
		return;
	}
	Vector<int> indices = p_state_machine->find_transition_to(current);
	int group_start_size = indices.size();
	if (group_start_size) {
		group_start_transition = p_state_machine->get_transition(indices[0]);
	} else {
		group_start_transition = Ref<AnimationNodeStateMachineTransition>();
	}
	indices = p_state_machine->find_transition_from(current);
	int group_end_size = indices.size();
	if (group_end_size) {
		group_end_transition = p_state_machine->get_transition(indices[0]);