Were nuclear weapons used in Khmelnytskyi? No, that's not true: the attack involved drones; none of the official reports includes information about the use of nuclear weapons.
The claim appeared in a video (archived here) where it was published by TikTok on May 15, 2023, under the title "Khmelnitskyi. Strike on the territory of the 'Kation' plant. Allegedly on the warehouses where shells with depleted uranium were." The text on the video says:
The use of nuclear weapons in Ukraine. An attack on an ammunition depot.
This is what the post looked like on TikTok at the time of writing:
(Source: TikTok screenshot taken on Sun May 21 10:27:42 2023 UTC)
The shelling, which took place in the early hours of Saturday, May 13, was widely reported in local and international media. Khmelnytskyi City Council reported that the attack involved drones. None of the official reports includes information about the use of nuclear weapons.
SaveEcoBot called the claims about the high radiation level in the region "fake news" and "Russian propaganda." It affirmed that the radiation level "did not exceed the natural one."
Eneregoatom, the National Nuclear Power Company of Ukraine, said in its official Telegram channel that "the radiation level at the industrial site [in Khmelnytskyi] and in the surrounding regions is at a level corresponding to the normal operation of power units and does not exceed natural background values."