I ran into this in 12.3, but it looks like it's still the case in HEAD. It looks like this is because `explain_get_index_name` in `explain.c` always quotes the index name, regardless of the format being used. I'd send a patch, but I'm not sure how `explain_get_index_name_hook` should fit into this.
Indeed, relation names should return the same. The fact that explain_get_index_name always calls quote_identifier is the culprit; it should call quote_identifier only when the format is TEXT. Patch is attached. I'm not sure if it should be backpatched to released versions because there should be applications that rely on this format. However, it would be good to backpatch it to v13 too.
