### 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 (updating_transitions) {
		return;
	}
	ERR_FAIL_COND(p_from == end_node || p_to == start_node);
	ERR_FAIL_COND(p_from == p_to);
	ERR_FAIL_COND(!_can_connect(p_from));
	ERR_FAIL_COND(!_can_connect(p_to));
	ERR_FAIL_COND(p_transition.is_null());
	for (int i = 0; i < transitions.size(); i++) {
		ERR_FAIL_COND(transitions[i].from == p_from && transitions[i].to == p_to);
	}
	updating_transitions = true;
	Transition tr;
	tr.from = p_from;
	tr.to = p_to;
	tr.transition = p_transition;
	tr.transition->connect("advance_condition_changed", callable_mp(this, &AnimationNodeStateMachine::_tree_changed), CONNECT_REFERENCE_COUNTED);
	transitions.push_back(tr);
	updating_transitions = false;
}
Ref<AnimationNodeStateMachineTransition> AnimationNodeStateMachine::get_transition(int p_transition) const {