### 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)

_reset_request_for_fading_from = false;
	bool is_state_changed = false;
	AnimationMixer::PlaybackInfo pi;
	NextInfo next;
	Vector<StringName> transition_path;
	transition_path.push_back(current);
	while (true) {
		next = _find_next(p_tree, p_state_machine);
		if (transition_path.has(next.node)) {
			WARN_PRINT_ONCE_ED("AnimationNodeStateMachinePlayback: " + base_path + "playback aborts the transition by detecting one or more looped transitions in the same frame to prevent to infinity loop. You may need to check the transition settings.");
			break; 
		}
		if (!_can_transition_to_next(p_tree, p_state_machine, next, p_test_only)) {
			break; 
		}
		transition_path.push_back(next.node);
		is_state_changed = true;
		
		if (next.xfade) {