### 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
TreeItem *troot = track_copy_select->create_item();
			for (int i = 0; i < animation->get_track_count(); i++) {
				NodePath path = animation->track_get_path(i);
				Node *node = nullptr;
				if (root && root->has_node(path)) {
					node = root->get_node(path);
				}
				String text;
				Ref<Texture2D> icon = get_editor_theme_icon(SNAME("Node"));
				if (node) {
					if (has_theme_icon(node->get_class(), EditorStringName(EditorIcons))) {
						icon = get_editor_theme_icon(node->get_class());
					}
					text = node->get_name();
					Vector<StringName> sn = path.get_subnames();
					for (int j = 0; j < sn.size(); j++) {
						text += ".";
						text += sn[j];
					}
					path = NodePath(node->get_path().get_names(), path.get_subnames(), true); 
				} else {
					text = path;
					int sep = text.find(":");
					if (sep != -1) {
						text = text.substr(sep + 1, text.length());
					}
				}
				String track_type;
				switch (animation->track_get_type(i)) {
					case Animation::TYPE_POSITION_3D: