### 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
AnimationTrackEditor *get_editor() const { return editor; }
	NodePath get_path() const;
	void set_animation_and_track(const Ref<Animation> &p_animation, int p_track, bool p_read_only);
	virtual Size2 get_minimum_size() const override;
	void set_timeline(AnimationTimelineEdit *p_timeline);
	void set_editor(AnimationTrackEditor *p_editor);
	void set_root(Node *p_root);
	void set_play_position(float p_pos);
	void update_play_position();
	void cancel_drop();
	void set_in_group(bool p_enable);
	void append_to_selection(const Rect2 &p_box, bool p_deselection);
	AnimationTrackEdit();
};
class AnimationTrackEditPlugin : public RefCounted {