### 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)

GDCLASS(AnimationRootNode, AnimationNode);
protected:
	virtual void _tree_changed();
	virtual void _animation_node_renamed(const ObjectID &p_oid, const String &p_old_name, const String &p_new_name);
	virtual void _animation_node_removed(const ObjectID &p_oid, const StringName &p_node);
public:
	AnimationRootNode() {}
};
class AnimationNodeStartState : public AnimationRootNode {
	GDCLASS(AnimationNodeStartState, AnimationRootNode);
};
class AnimationNodeEndState : public AnimationRootNode {
	GDCLASS(AnimationNodeEndState, AnimationRootNode);
};
class AnimationTree : public AnimationMixer {
	GDCLASS(AnimationTree, AnimationMixer);
#ifndef DISABLE_DEPRECATED
public:
	enum AnimationProcessCallback {
		ANIMATION_PROCESS_PHYSICS,
		ANIMATION_PROCESS_IDLE,
		ANIMATION_PROCESS_MANUAL,
	};
#endif 
private:
	Ref<AnimationRootNode> root_animation_node;