### 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)

virtual void get_parameter_list(List<PropertyInfo> *r_list) const;
	virtual Variant get_parameter_default_value(const StringName &p_parameter) const;
	virtual bool is_parameter_read_only(const StringName &p_parameter) const;
	void set_parameter(const StringName &p_name, const Variant &p_value);
	Variant get_parameter(const StringName &p_name) const;
	struct ChildNode {
		StringName name;
		Ref<AnimationNode> node;
	};
	virtual void get_child_nodes(List<ChildNode> *r_child_nodes);
	virtual String get_caption() const;
	virtual bool add_input(const String &p_name);
	virtual void remove_input(int p_index);
	virtual bool set_input_name(int p_input, const String &p_name);
	virtual String get_input_name(int p_input) const;
	int get_input_count() const;
	int find_input(const String &p_name) const;
	void set_filter_path(const NodePath &p_path, bool p_enable);
	bool is_path_filtered(const NodePath &p_path) const;
	void set_filter_enabled(bool p_enable);
	bool is_filter_enabled() const;
	void set_closable(bool p_closable);
	bool is_closable() const;
	virtual bool has_filter() const;
	virtual Ref<AnimationNode> get_child_by_name(const StringName &p_name) const;
	Ref<AnimationNode> find_node_by_path(const String &p_name) const;
	AnimationNode();
};
VARIANT_ENUM_CAST(AnimationNode::FilterAction)
class AnimationRootNode : public AnimationNode {