For the briber to hire a family member of the bribed, and pay him huge amounts of money for nothing, is a time honored method of bribing literally going back centuries ... likely millenia.
Rather interesting that you'd evoke the question of "proof."
The argument would be a lot more solid if there was no good reason, other than a corrupt one, to make firing Shokin a prerequisite for a $1b+ in loan.
That's just not the case though.
The whole thing is really about the EU/USA vs Russia.
Ukraine was recovering from just ousting an extremely corrupt president who had Putins full support.
Russia had just been kicked from the G9 (now G8) for invading Ukraine and annexing crimea.
Shokin had a record of being very pro Russia and very corrupt. He blocked the prosecution of a bunch of guys who open fired on a Ukrainian Independence protest. He blocked the prosecution of a bunch other prosecutors who were caught taking bribes. Yet he raided and prosecuted anti Russian groups for anything he could find.
Basically, he was an obstacle in Ukraines fight for independence from Russia.
The US and the EU considered helping Ukraine maintain their independence a matter of international security. So did the IMF, EBRD and a bunch of other international organizations.
All of these countries and organizations also considered Shokin a serious threat to Ukraines future.
The Obama administration (not Biden) decided that loaning Ukraine the money while Shokin was still in power would make things worse, not better.
Biden went over and convinced them to fire him. Then he bragged about it because he accomplished something that most of the world was hoping would happen.