### Godot version

v4.0.beta.custom_build [cc7aa72f0], v3.5.1.stable.official [6fed1ffa3]

### System information

Windows 10

### Issue description

`AnimationTree.rename_parameter` doesn't work when called from gdscript. It should rename AnimationTree's nodes. I have confirmed from the source how to call this and what parameters the editor uses when renaming nodes from the editor. For some reason, even when using the same parameters in gdscript, nothing happens.

I'm not sure if is this regression (if it is, it's quite old) or has it ever been tested to work. Seems a bit obscure method to be exposed anyway, unless somebody wants to make a custom editor plugin for AnimationTree. I ran into the issue trying to add class reference description for it.

### Steps to reproduce

* Add AnimationTree with any parameter named `CurrentName`
* Call following code:
```
rename_parameter("parameters/CurrentName", "parameters/NewName")
```


### Minimal reproduction project

[Rename Parameter bug.zip](https://github.com/godotengine/godot/files/10513522/Rename.Parameter.bug.zip)

bool started = true;
	NodePath root_motion_track;
	Vector3 root_motion_position = Vector3(0, 0, 0);
	Quaternion root_motion_rotation = Quaternion(0, 0, 0, 1);
	Vector3 root_motion_scale = Vector3(0, 0, 0);
	friend class AnimationNode;
	bool properties_dirty = true;
	void _tree_changed();
	void _update_properties();
	List<PropertyInfo> properties;
	HashMap<StringName, HashMap<StringName, StringName>> property_parent_map;
	HashMap<StringName, Pair<Variant, bool>> property_map; 
	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;
	void _update_properties_for_node(const String &p_base_path, Ref<AnimationNode> node);
	ObjectID last_animation_player;
protected:
	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;
	void _notification(int p_what);
	static void _bind_methods();
	GDVIRTUAL5RC(Variant, _post_process_key_value, Ref<Animation>, int, Variant, Object *, int);
	Variant post_process_key_value(const Ref<Animation> &p_anim, int p_track, Variant p_value, const Object *p_object, int p_object_idx = -1);
	virtual Variant _post_process_key_value(const Ref<Animation> &p_anim, int p_track, Variant p_value, const Object *p_object, int p_object_idx = -1);
public: