### Godot version

4.0.stable

### System information

Windows 10, Forward+, GTX 1070 driver 528.49

### Issue description

When trying to edit the handle mode of a bezier cruve key from the inspector tab, the mode doesn't change. It works fine when right clicking on the key and setting the handle mode from here though. 

https://user-images.githubusercontent.com/24484962/222379540-29d71b6d-ff0c-4a21-9905-9750d0581fda.mp4



### Steps to reproduce

On an animation track using a bezier curve, select a key and try to change the handle mode from the inspector tab

### Minimal reproduction project

N/A
GDCLASS(AnimationMultiTrackKeyEdit, Object);
public:
	bool setting = false;
	bool animation_read_only = false;
	Ref<Animation> animation;
	RBMap<int, List<float>> key_ofs_map;
	RBMap<int, NodePath> base_map;
	PropertyInfo hint;
	Node *root_path = nullptr;
	bool use_fps = false;
	bool _hide_script_from_inspector() { return true; }
	bool _hide_metadata_from_inspector() { return true; }
	bool _dont_undo_redo() { return true; }
	bool _is_read_only() { return animation_read_only; }
	void notify_change();
	Node *get_root_path();
	void set_use_fps(bool p_enable);
protected:
	static void _bind_methods();
	void _fix_node_path(Variant &value, NodePath &base);
	void _update_obj(const Ref<Animation> &p_anim);
	void _key_ofs_changed(const Ref<Animation> &p_anim, float from, float to);
	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;
};
class AnimationTimelineEdit : public Range {