### 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
AnimationTimelineEdit *timeline = nullptr;
	Popup *path_popup = nullptr;
	LineEdit *path = nullptr;
	Node *root = nullptr;
	Control *play_position = nullptr; 
	float play_position_pos = 0.0f;
	NodePath node_path;
	Ref<Animation> animation;
	bool read_only = false;
	int track = 0;
	Rect2 check_rect;
	Rect2 path_rect;
	Rect2 update_mode_rect;
	Rect2 interp_mode_rect;
	Rect2 loop_wrap_rect;
	Rect2 remove_rect;
	Ref<Texture2D> type_icon;
	Ref<Texture2D> selected_icon;
	PopupMenu *menu = nullptr;
	bool hovered = false;
	bool clicking_on_name = false;
	int hovering_key_idx = -1;
	void _zoom_changed();
	Ref<Texture2D> icon_cache;
	String path_cache;
	void _menu_selected(int p_index);
	void _path_submitted(const String &p_text);
	void _play_position_draw();
	bool _is_value_key_valid(const Variant &p_key_value, Variant::Type &r_valid_type) const;
	Ref<Texture2D> _get_key_type_icon() const;