> Actually even better I think it should be `source.store(session)`

This means "store session on source", which the implementation actually does. Image `item.append(list)` or `obj.__set__("attr", value)`, which would translate to `value.attr = obj`. At least is should be `source.store_to(session)` to indicate that `.store_to` is a right associative operator. But really `session.store(source)` is the correct order.