### 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)

NodePath advance_expression_base_node = NodePath(String("."));
	AnimationNode::ProcessState process_state;
	uint64_t process_pass = 1;
	bool started = true;
	friend class AnimationNode;
	List<PropertyInfo> properties;
	HashMap<StringName, HashMap<StringName, StringName>> property_parent_map;
	HashMap<ObjectID, StringName> property_reference_map;
	HashMap<StringName, Pair<Variant, bool>> property_map; 
	bool properties_dirty = true;
	void _update_properties();
	void _update_properties_for_node(const String &p_base_path, Ref<AnimationNode> p_node);
	void _tree_changed();
	void _animation_node_renamed(const ObjectID &p_oid, const String &p_old_name, const String &p_new_name);
	void _animation_node_removed(const ObjectID &p_oid, const StringName &p_node);
	struct Activity {
		uint64_t last_pass = 0;
		real_t activity = 0.0;
	};
	HashMap<StringName, Vector<Activity>> input_activity_map;
	HashMap<StringName, Vector<Activity> *> input_activity_map_get;
	NodePath animation_player;
	void _setup_animation_player();
	void _animation_player_changed();
	bool _set(const StringName &p_name, const Variant &p_value);
	bool _get(const StringName &p_name, Variant &r_ret) const;
	void _get_property_list(List<PropertyInfo> *p_list) const;
	virtual void _validate_property(PropertyInfo &p_property) const override;
	void _notification(int p_what);
	static void _bind_methods();