I've never heard that よう is a copula, where did you get that from?
In any case, this よう is the same as in ADoBJG entry for yōda , just in the polite form.
よう generally is a suffix that expresses seeming or similarity (in this case 'seeming').
The result of a よう suffix can be considered a な adjective, and ~よう is used in all the ways a な adjective is, but the meaning of those changes may not be obvious, which is why there are so many grammar points around things like ような・ように・ようにする・ようだ .