### 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 _set_active(bool p_active) override;
	
	virtual bool _blend_pre_process(double p_delta, int p_track_count, const HashMap<NodePath, int> &p_track_map) override;
#ifndef DISABLE_DEPRECATED
	void _set_process_callback_bind_compat_80813(AnimationProcessCallback p_mode);
	AnimationProcessCallback _get_process_callback_bind_compat_80813() const;
	void _set_tree_root_bind_compat_80813(const Ref<AnimationNode> &p_root);
	Ref<AnimationNode> _get_tree_root_bind_compat_80813() const;
	static void _bind_compatibility_methods();
#endif 
public:
	void set_animation_player(const NodePath &p_path);
	NodePath get_animation_player() const;
	void set_root_animation_node(const Ref<AnimationRootNode> &p_animation_node);
	Ref<AnimationRootNode> get_root_animation_node() const;
	void set_advance_expression_base_node(const NodePath &p_path);
	NodePath get_advance_expression_base_node() const;
	PackedStringArray get_configuration_warnings() const override;
	bool is_state_invalid() const;
	String get_invalid_state_reason() const;
	real_t get_connection_activity(const StringName &p_path, int p_connection) const;
	uint64_t get_last_process_pass() const;
	AnimationTree();
	~AnimationTree();
};
#ifndef DISABLE_DEPRECATED
VARIANT_ENUM_CAST(AnimationTree::AnimationProcessCallback);
#endif 
#endif