### 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
void _zoom_callback(float p_zoom_factor, Vector2 p_origin, Ref<InputEvent> p_event);
	bool dragging_timeline = false;
	bool dragging_hsize = false;
	float dragging_hsize_from = 0.0f;
	float dragging_hsize_at = 0.0f;
	virtual void gui_input(const Ref<InputEvent> &p_event) override;
	void _track_added(int p_track);
protected:
	static void _bind_methods();
	void _notification(int p_what);
public:
	int get_name_limit() const;
	int get_buttons_width() const;
	float get_zoom_scale() const;
	virtual Size2 get_minimum_size() const override;
	void set_animation(const Ref<Animation> &p_animation, bool p_read_only);
	void set_track_edit(AnimationTrackEdit *p_track_edit);
	void set_zoom(Range *p_zoom);
	Range *get_zoom() const { return zoom; }
	void set_play_position(float p_pos);
	float get_play_position() const;
	void update_play_position();
	void update_values();
	void set_use_fps(bool p_use_fps);
	bool is_using_fps() const;
	void set_hscroll(HScrollBar *p_hscroll);
	virtual CursorShape get_cursor_shape(const Point2 &p_pos) const override;
	AnimationTimelineEdit();
};
class AnimationTrackEdit : public Control {