### 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)

animation_player = p_path;
	if (p_path.is_empty()) {
		set_root_node(SceneStringNames::get_singleton()->path_pp);
		while (animation_libraries.size()) {
			remove_animation_library(animation_libraries[0].name);
		}
	}
#ifdef 
	emit_signal(SNAME("animation_player_changed")); // 
	emit_signal(SNAME("mixer_updated"));
#endif // 
	_setup_animation_player();
	notify_property_list_changed();
}
NodePath AnimationTree::get_animation_player() const {
	return animation_player;
}
void AnimationTree::_setup_animation_player() {
	if (!is_inside_tree()) {
		return;
	}
	cache_valid = false;
	if (animation_player.is_empty()) {