### 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)

return transitions.size();
}
void AnimationNodeStateMachine::remove_transition(const StringName &p_from, const StringName &p_to) {
	for (int i = 0; i < transitions.size(); i++) {
		if (transitions[i].from == p_from && transitions[i].to == p_to) {
			remove_transition_by_index(i);
			return;
		}
	}
}
void AnimationNodeStateMachine::remove_transition_by_index(const int p_transition) {
	ERR_FAIL_INDEX(p_transition, transitions.size());
	Transition tr = transitions[p_transition];
	transitions.write[p_transition].transition->disconnect("advance_condition_changed", callable_mp(this, &AnimationNodeStateMachine::_tree_changed));
	transitions.remove_at(p_transition);
	Vector<String> path_from = String(tr.from).split("/");
	Vector<String> path_to = String(tr.to).split("/");
	List<Vector<String>> paths;
	paths.push_back(path_from);
	paths.push_back(path_to);
}
void AnimationNodeStateMachine::_remove_transition(const Ref<AnimationNodeStateMachineTransition> p_transition) {