### 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)

states.clear();
	transitions.clear();
	playback = "playback";
	start_node = "Start";
	end_node = "End";
	graph_offset = Vector2();
	Ref<AnimationNodeStartState> s;
	s.instantiate();
	State start;
	start.node = s;
	start.position = Vector2(200, 100);
	states[start_node] = start;
	Ref<AnimationNodeEndState> e;
	e.instantiate();
	State end;
	end.node = e;
	end.position = Vector2(900, 100);
	states[end_node] = end;
	emit_changed();
	emit_signal(SNAME("tree_changed"));
}
void AnimationNodeStateMachine::set_node_position(const StringName &p_name, const Vector2 &p_position) {
	ERR_FAIL_COND(!states.has(p_name));
	states[p_name].position = p_position;
}
Vector2 AnimationNodeStateMachine::get_node_position(const StringName &p_name) const {
	ERR_FAIL_COND_V(!states.has(p_name), Vector2());
	return states[p_name].position;
}
void AnimationNodeStateMachine::_tree_changed() {