### 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
for (int i = 0; i < p_animation->get_track_count(); i++) {
		bool prop_exists = false;
		Variant::Type valid_type = Variant::NIL;
		Object *obj = nullptr;
		Ref<Resource> res;
		Vector<StringName> leftover_path;
		Node *node = root->get_node_and_resource(p_animation->track_get_path(i), res, leftover_path);
		if (res.is_valid()) {
			obj = res.ptr();
		} else if (node) {
			obj = node;
		}
		if (obj && p_animation->track_get_type(i) == Animation::TYPE_VALUE) {
			valid_type = obj->get_static_property_type_indexed(leftover_path, &prop_exists);
		}
		if (!obj && cleanup_tracks->is_pressed()) {
			p_animation->remove_track(i);
			i--;
			continue;
		}
		if (!prop_exists || p_animation->track_get_type(i) != Animation::TYPE_VALUE || !cleanup_keys->is_pressed()) {
			continue;
		}
		for (int j = 0; j < p_animation->track_get_key_count(i); j++) {
			Variant v = p_animation->track_get_key_value(i, j);
			if (!Variant::can_convert(v.get_type(), valid_type)) {
				p_animation->track_remove_key(i, j);
				j--;
			}
		}