-구나 in 미안하구나 just expresses her realization that she was sorry for abandoning him when he was a baby. I think that she never realized before that she was actually sorry for leaving him. So, like what you said, -구나 expresses something you have encountered for the first time. In other words, it's something you have realized for the first time :).
If you want to translate 미안하구나 with it's nuance, you could say "I know that I'm actually sorry now".