### 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
String val_hint_string;
						if (v.get_type() == Variant::OBJECT) {
							
							Ref<Resource> res = v;
							if (res.is_valid()) {
								val_hint = PROPERTY_HINT_RESOURCE_TYPE;
								val_hint_string = res->get_class();
							}
						}
						if (v.get_type() != Variant::NIL) {
							p_list->push_back(PropertyInfo(v.get_type(), "value", val_hint, val_hint_string));
						}
					}
				}
				p_list->push_back(PropertyInfo(Variant::FLOAT, "easing", PROPERTY_HINT_EXP_EASING));
			} break;
			case Animation::TYPE_METHOD: {
				p_list->push_back(PropertyInfo(Variant::STRING_NAME, "name"));
				p_list->push_back(PropertyInfo(Variant::INT, "arg_count", PROPERTY_HINT_RANGE, "0,32,1,or_greater"));
				Dictionary d = animation->track_get_key_value(first_track, first_key);
				ERR_FAIL_COND(!d.has("args"));
				Vector<Variant> args = d["args"];
				String vtypes;
				for (int i = 0; i < Variant::VARIANT_MAX; i++) {
					if (i > 0) {
						vtypes += ",";
					}
					vtypes += Variant::get_type_name(Variant::Type(i));
				}
				for (int i = 0; i < args.size(); i++) {