The use of the word officially is unnessecary, but neither sounds wrong.

Basically, yes. But ... officially over... is the more usual. Officially through... sounds a little strange. I think it might be because 'officially' sounds formal, whereas the 'through' is part of the much more informal ... we're through! That's it. I've had enough. Goodbye. I realize that the other form is pairing 'officially' with a phrasal verb - but it's said so often that it does not sound strange. You'll have to sound out other people's opinions.

Yes. But the sentence with 'through' is a but more American.