### 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
mutable int dropping_at = 0;
	float insert_at_pos = 0.0f;
	bool moving_selection_attempt = false;
	int select_single_attempt = -1;
	bool moving_selection = false;
	float moving_selection_from_ofs = 0.0f;
	bool in_group = false;
	AnimationTrackEditor *editor = nullptr;
protected:
	static void _bind_methods();
	void _notification(int p_what);
	virtual void gui_input(const Ref<InputEvent> &p_event) override;
public:
	virtual Variant get_drag_data(const Point2 &p_point) override;
	virtual bool can_drop_data(const Point2 &p_point, const Variant &p_data) const override;
	virtual void drop_data(const Point2 &p_point, const Variant &p_data) override;
	virtual String get_tooltip(const Point2 &p_pos) const override;
	virtual int get_key_height() const;
	virtual Rect2 get_key_rect(int p_index, float p_pixels_sec);
	virtual bool is_key_selectable_by_distance() const;
	virtual void draw_key_link(int p_index, float p_pixels_sec, int p_x, int p_next_x, int p_clip_left, int p_clip_right);
	virtual void draw_key(int p_index, float p_pixels_sec, int p_x, bool p_selected, int p_clip_left, int p_clip_right);
	virtual void draw_bg(int p_clip_left, int p_clip_right);
	virtual void draw_fg(int p_clip_left, int p_clip_right);
	
	void draw_texture_region_clipped(const Ref<Texture2D> &p_texture, const Rect2 &p_rect, const Rect2 &p_region);
	void draw_rect_clipped(const Rect2 &p_rect, const Color &p_color, bool p_filled = true);
	int get_track() const;
	Ref<Animation> get_animation() const;
	AnimationTimelineEdit *get_timeline() const { return timeline; }