"Yay! Good luck!"
For "Good luck!" one could also say "Lykkyä tykö!" [Luck to(ward) you]. A bit of a pronunciation nightmare though, which might be a reason for not introducing it at this point. :D But for those, who are already familiar with y, ä & ö, or like a challenge, now you know it's there (even if not so often used nowadays).
Onnea is luck in partitive and of course good luck unless someone specifically says it's bad. Used for "(I wish you) good luck!" - "Onnea!". When wishing luck you'd often add what it was wished for and this way you can also add paljon if you want. Just "Paljon onnea" alone is a phrase for congratulations.
If it wasn't a phrase for congratulations it could work like this too. But literally paljon onnea is lots of happiness / lots of luck. The latter would be used the same way as in English "I wish you lots of luck..." - "Toivon sinulle paljon onnea..." where in the end you add what it's wished for. The Finnish birthday song repeats Paljon onnea (literally lots of happiness) so it really is a phrase for congratulations if mentioned without other specifications.
I can accept this but, if true, then the "Tips" section for this lesson is highly misleading, as it says:
"The Finnish expressions onnea and paljon onnea can be used both to wish someone good luck and to congratulate them."
It specifically say that they can "BOTH" be used to wish good luck. I'm not saying you're wrong but, if you're right, then the Tips section must necessarily be either wrong or at least lacking specificity.
I sadly can't affect the tips section since I didn't qualify to help. I have found also a few other things in the course a bit confusing and too area specific. Finnish is a rich language and it can be difficult for the contributors to not show their cultural area through the word choices.