### 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)

stop_request = true;
}
bool AnimationNodeStateMachinePlayback::is_playing() const {
	return playing;
}
bool AnimationNodeStateMachinePlayback::is_end() const {
	return current == "End" && fading_from == StringName();
}
StringName AnimationNodeStateMachinePlayback::get_current_node() const {
	return current;
}
StringName AnimationNodeStateMachinePlayback::get_fading_from_node() const {
	return fading_from;
}
Vector<StringName> AnimationNodeStateMachinePlayback::get_travel_path() const {
	return path;
}
TypedArray<StringName> AnimationNodeStateMachinePlayback::_get_travel_path() const {
	return Variant(get_travel_path()).operator Array();
}
float AnimationNodeStateMachinePlayback::get_current_play_pos() const {
	return pos_current;
}
float AnimationNodeStateMachinePlayback::get_current_length() const {
	return len_current;
}
float AnimationNodeStateMachinePlayback::get_fade_from_play_pos() const {
	return pos_fade_from;
}
float AnimationNodeStateMachinePlayback::get_fade_from_length() const {