It was his private jet, as you said. Not the only one he owns. It was an Embraer business class jet. Very well-made aircraft designed and built in Brazil. Embraer is heavily subsidized by the Brazilian government. Their jets have become very popular and are extensively used by United, American, Delta, and other U.S. carriers for commuter jet service.
It was ONE of his private jets. Another landed in another town later in the day; there’s some speculation on Telegram that Prighozin was on the second jet, and is still alive.
Belarus has apparently got a bit worried about the Wagner chatter, and shut off internet access around their locations. Not before Wagner put out some messages to the effect of, stuff’s gonna happen now. Some speculation that they’ll be bugging out of Belarus before the end of the week.