### 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)

path.clear();
}
void AnimationNodeStateMachinePlayback::push_path(const StringName &p_state) {
	path.push_back(p_state);
}
void AnimationNodeStateMachinePlayback::_set_base_path(const String &p_base_path) {
	base_path = p_base_path;
}
Ref<AnimationNodeStateMachinePlayback> AnimationNodeStateMachinePlayback::_get_parent_playback(AnimationTree *p_tree) const {
	if (base_path.is_empty()) {
		return Ref<AnimationNodeStateMachinePlayback>();
	}
	Vector<String> split = base_path.split("/");
	ERR_FAIL_COND_V_MSG(split.size() < 2, Ref<AnimationNodeStateMachinePlayback>(), "Path is too short.");
	StringName self_path = split[split.size() - 2];
	split.remove_at(split.size() - 2);
	String playback_path = String("/").join(split) + "playback";
	Ref<AnimationNodeStateMachinePlayback> playback = p_tree->get(playback_path);
	if (!playback.is_valid()) {
		ERR_PRINT_ONCE("Can't get parent AnimationNodeStateMachinePlayback with path: " + playback_path + ". Maybe there is no Root/Nested AnimationNodeStateMachine in the parent of the Grouped AnimationNodeStateMachine.");
		return Ref<AnimationNodeStateMachinePlayback>();
	}
	if (playback->get_current_node() != self_path) {
		return Ref<AnimationNodeStateMachinePlayback>();
	}
	return playback;
}
Ref<AnimationNodeStateMachine> AnimationNodeStateMachinePlayback::_get_parent_state_machine(AnimationTree *p_tree) const {