The record for the most overtakes in a single race belongs to China in 2016 with a tally of 161.
In contrast, a number of races didn't record a single overtake - 2003 Monaco Grand Prix, 2005 US Grand Prix, 2009 European Grand Prix, 2021 Monaco Grand Prix, 2021 Belgian Grand Prix.
Read a great article about overtake records by Joe Holding on autosport.com - here