### 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)

}
	if (current != p_state_machine->start_node && p_next.switch_mode == AnimationNodeStateMachineTransition::SWITCH_MODE_AT_END) {
		return pos_current >= len_current - p_next.xfade;
	}
	return true;
}
Ref<AnimationNodeStateMachineTransition> AnimationNodeStateMachinePlayback::_check_group_transition(AnimationTree *p_tree, AnimationNodeStateMachine *p_state_machine, const AnimationNodeStateMachine::Transition &p_transition, Ref<AnimationNodeStateMachine> &r_state_machine, bool &r_bypass) const {
	Ref<AnimationNodeStateMachineTransition> temp_transition;
	Ref<AnimationNodeStateMachinePlayback> parent_playback;
	if (r_state_machine->get_state_machine_type() == AnimationNodeStateMachine::STATE_MACHINE_TYPE_GROUPED) {
		if (p_transition.from == "Start") {
			parent_playback = _get_parent_playback(p_tree);
			if (parent_playback.is_valid()) {
				r_bypass = true;
				temp_transition = parent_playback->_get_group_start_transition();
			}
		} else if (p_transition.to == "End") {
			parent_playback = _get_parent_playback(p_tree);
			if (parent_playback.is_valid()) {
				temp_transition = parent_playback->_get_group_end_transition();
			}
		}
		if (temp_transition.is_valid()) {
			r_state_machine = _get_parent_state_machine(p_tree);
			return temp_transition;
		}
	}
	return p_transition.transition;
}
AnimationNodeStateMachinePlayback::NextInfo AnimationNodeStateMachinePlayback::_find_next(AnimationTree *p_tree, AnimationNodeStateMachine *p_state_machine) const {