Successfully means in a way that achieved what was wanted. Successfully completed, successfully argued, treated successfully.
It reports the outcome and not the manner, which is why it goes with verbs of achieving. In official writing it does a lot of quiet work: successfully completed says the thing was finished and not that it was done well.
1adverbsuccessfullyIn a way that achieved what was wanted.
“The surgeons successfully removed the tumour, and she is recovering well.”
successfully is a manner.
From successful + -ly.
Etymology from Wiktionary, CC BY-SA