### 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)

int auto_advance_to = -1;
		float priority_best = 1e20;
		for (int i = 0; i < p_state_machine->transitions.size(); i++) {
			Ref<AnimationNodeStateMachine> anodesm = p_state_machine;
			bool bypass = false;
			Ref<AnimationNodeStateMachineTransition> ref_transition = _check_group_transition(p_tree, p_state_machine, p_state_machine->transitions[i], anodesm, bypass);
			if (ref_transition->get_advance_mode() == AnimationNodeStateMachineTransition::ADVANCE_MODE_DISABLED) {
				continue;
			}
			if (p_state_machine->transitions[i].from == current && (_check_advance_condition(anodesm, ref_transition) || bypass)) {
				if (ref_transition->get_priority() <= priority_best) {
					priority_best = ref_transition->get_priority();
					auto_advance_to = i;
				}
			}
		}
		if (auto_advance_to != -1) {
			next.node = p_state_machine->transitions[auto_advance_to].to;
			Ref<AnimationNodeStateMachine> anodesm = p_state_machine;
			bool bypass = false;
			Ref<AnimationNodeStateMachineTransition> ref_transition = _check_group_transition(p_tree, p_state_machine, p_state_machine->transitions[auto_advance_to], anodesm, bypass);
			next.xfade = ref_transition->get_xfade_time();
			next.curve = ref_transition->get_xfade_curve();
			next.switch_mode = ref_transition->get_switch_mode();
			next.is_reset = ref_transition->is_reset();
		}
	}
	return next;
}
bool AnimationNodeStateMachinePlayback::_check_advance_condition(const Ref<AnimationNodeStateMachine> state_machine, const Ref<AnimationNodeStateMachineTransition> transition) const {