'As of yet' implies that it still hasn't happened. Where as 'until now' implies that it just happened.
E.g. Have you done it?
"I haven't done it as of yet"
That means I have not done it yet, but I intend to do it soon or in the future.
E.g. Have you done it?
"I had not done it until now"
Implies that you just did it (but you were probably a little bit late).
Another example:
Did you see the film Parasite?
"I have not seen it as of yet" - this means I haven't seen it, but I want to / I will
"I had not seen it until now" - this means that I have just seen it (even though it was a little bit late and I wanted to see it earlier)
Hope that helps :)