According to the EU's 'EU vs Disinfo' task force, claims that millions of dollars are funneled into Zelensky's office are false, though it doesn't specifically mention the $10 billion annual figure. In fact, I cannot find that $10 billion number anywhere other than in the linked APT interview with Ukrainian MP Artem Dmytruk, which is then regurgitated on social media and in forums.
It is true that there are corruption concerns surrounding Zelensky's government. The EU recently withheld aid after Zelensky stripped the independence of two anticorruption agencies. According to the New York Times, however, those anticorruption agencies had been investigating senior officials in Zelensky's government, not Zelensky himself. This includes former deputy prime minister Oleksiy Chernyshov, who was charged with corruption on June 23 and accused of taking kickbacks in a real-estate deal—rather than stealing foreign aid or tax dollars.
Politifact, in February 2025, also examined similar claims that some US aid intended for Ukraine had been stolen by Ukrainian officials and generals (or by the CIA). Without more substantiating evidence, this claim is false.