### 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
EDIT_COPY_TRACKS,
		EDIT_COPY_TRACKS_CONFIRM,
		EDIT_PASTE_TRACKS,
		EDIT_SCALE_SELECTION,
		EDIT_SCALE_FROM_CURSOR,
		EDIT_SCALE_CONFIRM,
		EDIT_EASE_SELECTION,
		EDIT_EASE_CONFIRM,
		EDIT_DUPLICATE_SELECTION,
		EDIT_DUPLICATE_TRANSPOSED,
		EDIT_ADD_RESET_KEY,
		EDIT_DELETE_SELECTION,
		EDIT_GOTO_NEXT_STEP,
		EDIT_GOTO_NEXT_STEP_TIMELINE_ONLY, 
		EDIT_GOTO_PREV_STEP,
		EDIT_APPLY_RESET,
		EDIT_BAKE_ANIMATION,
		EDIT_BAKE_ANIMATION_CONFIRM,
		EDIT_OPTIMIZE_ANIMATION,
		EDIT_OPTIMIZE_ANIMATION_CONFIRM,
		EDIT_CLEAN_UP_ANIMATION,
		EDIT_CLEAN_UP_ANIMATION_CONFIRM
	};
	void add_track_edit_plugin(const Ref<AnimationTrackEditPlugin> &p_plugin);
	void remove_track_edit_plugin(const Ref<AnimationTrackEditPlugin> &p_plugin);
	void set_animation(const Ref<Animation> &p_anim, bool p_read_only);
	Ref<Animation> get_current_animation() const;
	void set_root(Node *p_root);
	Node *get_root() const;
	void update_keying();