### 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 (p_next.node == StringName()) {
		return false;
	}
	if (next_request) {
		
		next_request = false;
		
		Ref<AnimationNodeStateMachine> anodesm = p_state_machine->find_node_by_path(current);
		if (anodesm.is_valid() && anodesm->get_state_machine_type() == AnimationNodeStateMachine::STATE_MACHINE_TYPE_GROUPED) {
			Ref<AnimationNodeStateMachinePlayback> playback = p_tree->get(base_path + current + "/playback");
			ERR_FAIL_COND_V(!playback.is_valid(), false);
			playback->_set_base_path(base_path + current + "/");
			if (p_test_only) {
				playback = playback->duplicate();
			}
			playback->_next_main();
			
			fading_from = StringName();
			fading_pos = 0;
		} else {
			return true;
		}
	}
	if (fading_from != StringName()) {
		return false;