### 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
bool has_keying() const;
	Dictionary get_state() const;
	void set_state(const Dictionary &p_state);
	void cleanup();
	void set_anim_pos(float p_pos);
	void insert_node_value_key(Node *p_node, const String &p_property, const Variant &p_value, bool p_only_if_exists = false);
	void insert_value_key(const String &p_property, const Variant &p_value, bool p_advance);
	void insert_transform_key(Node3D *p_node, const String &p_sub, const Animation::TrackType p_type, const Variant p_value);
	bool has_track(Node3D *p_node, const String &p_sub, const Animation::TrackType p_type);
	void make_insert_queue();
	void commit_insert_queue();
	void show_select_node_warning(bool p_show);
	void show_dummy_player_warning(bool p_show);
	void show_inactive_player_warning(bool p_show);
	bool is_key_selected(int p_track, int p_key) const;
	bool is_selection_active() const;
	bool is_moving_selection() const;
	bool is_snap_enabled() const;
	float get_moving_selection_offset() const;
	float snap_time(float p_value, bool p_relative = false);
	bool is_grouping_tracks();
	
	void goto_prev_step(bool p_from_mouse_event);
	
	void goto_next_step(bool p_from_mouse_event, bool p_timeline_only = false);
	MenuButton *get_edit_menu();
	AnimationTrackEditor();
	~AnimationTrackEditor();
};
class AnimationTrackKeyEditEditor : public EditorProperty {