No matter the Biden Administration's motivations in publicising its role in what western media is celebrating as a success story — presumably, with an eye on domestic politics in America — it could be factually correct. The media leak puts the dramatic happenings in the past 3-4 days in proper perspective. 

There are two ways of looking at the surge by the Ukrainian military: one, Kiev has inflicted a heavy defeat on the Russians and forced them to retreat, or, the American intelligence finally got wind of the unobtrusive thinning out of the Russian frontline in Kharkov that had been going on in the recent weeks as part of a larger re-deployment of military formations, and shared the intelligence with Kiev, who of course gleefully acted on it. 

The New York Times report effectively confirms the latter reading of the situation, which has been the stuff of hearsay and whispers so far. 

Indeed, there has been hardly any fighting as such in Kharkov region during this Ukrainian surge, and the Russian focus was, unsurprisingly, to pull out the residual forces in the frontline under the cover of heavy artillery fire. The Russian operation ensured that there was no significant casualty. The new frontline that was being steadily put together in the recent weeks (or months) along the Oskol River has crystallised.