Does "Onnea" break down into "good" and "luck" in some way?
Onnea is the partitive form of the word onni. Onni means both (good) luck and happiness. "Onnea!" is how we wish good luck to other people in Finnish.
Wiktionary article about onni: https://en.wiktionary.org/wiki/onni#Finnish
Best wishes, Liisa is wrong?