Well see, in the first article, this chap says this:Please point out in either of the articles attached where this exact claim was made.
Yaroslavskyi, who heads a Ukrainian Special Reconnaissance Unit, told the BBC that at least some defenses promised by officials were missing in Kharkiv.
"Either it was an act of negligence, or corruption. It wasn't a failure. It was a betrayal," he said, per the outlet.
And the second article says this:
The U.S. State Department does "not anticipate any major breakthroughs" by Russia toward Kharkiv, but Russia may "make further advances in the coming weeks," Deputy Spokesperson Vedant Patel said during a press briefing on May 13.
U.S. President Joe Biden authorized a $400 million military aid package for Ukraine on May 10, after Congress approved a long-awaited $61 billion spending bill for Kyiv in April.
So saying "a billion" going towards the second largest city seems pretty fair.