### 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
NodePath full_path;
		NodePath base_path;
		Animation::TrackType track_type = Animation::TYPE_ANIMATION;
		Animation::InterpolationType interp_type = Animation::INTERPOLATION_CUBIC_ANGLE;
		Animation::UpdateMode update_mode = Animation::UPDATE_CAPTURE;
		Animation::LoopMode loop_mode = Animation::LOOP_PINGPONG;
		bool loop_wrap = false;
		bool enabled = false;
		bool use_blend = false;
		struct Key {
			float time = 0;
			float transition = 0;
			Variant value;
		};
		Vector<Key> keys;
	};
	Vector<TrackClipboard> track_clipboard;
	void _insert_animation_key(NodePath p_path, const Variant &p_value);
	void _pick_track_filter_text_changed(const String &p_newtext);
	void _pick_track_select_recursive(TreeItem *p_item, const String &p_filter, Vector<Node *> &p_select_candidates);
	void _pick_track_filter_input(const Ref<InputEvent> &p_ie);
protected:
	static void _bind_methods();
	void _notification(int p_what);
public:
	
	void _clear_selection(bool p_update = false);
	void _key_selected(int p_key, bool p_single, int p_track);
	void _key_deselected(int p_key, int p_track);
	enum {