### 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)

ERR_FAIL_NULL_V(node_state.parent, 0);
		new_parent = node_state.parent;
		new_path = String(new_parent->node_state.base_path) + String(p_subpath) + "/";
	}
	// 
	// 
	p_node->node_state.base_path = new_path;
	p_node->node_state.parent = new_parent;
	if (!p_playback_info.seeked && !p_sync && !any_valid) {
		p_playback_info.time = 0.0;
		return p_node->_pre_process(process_state, p_playback_info);
	}
	return p_node->_pre_process(process_state, p_playback_info);
}
String AnimationNode::get_caption() const {
	String ret = "Node";
	GDVIRTUAL_CALL(_get_caption, ret);
	return ret;
}
bool AnimationNode::add_input(const String &p_name) {
	// 
	ERR_FAIL_COND_V(Object::cast_to<AnimationRootNode>(this) != nullptr, false);
	Input input;
	ERR_FAIL_COND_V(p_name.contains(".") || p_name.contains("/"), false);
	input.name = p_name;
	inputs.push_back(input);
	emit_changed();
	return true;
}
void AnimationNode::remove_input(int p_index) {