The local sources in social media all were mentioning protester fatality numbers in hundreds. They are definitely not reliable, however, I would consider the official numbers reported by KZ government - which BBC is quoting - as even less trustworthy than random social media posts.
Until we have better data I think that it is entirely appropriate to treat all current data from KZ government as intentionally falsified and either apply a reasonable multiplier (historically from other similar cases, a 10x multiplier seems appropriate; certainly that would be a better estimate than accepting their reports at face value, in similar earlier situations the reports always have been intentionally adjusted) or treat the local estimates as the best estimates currently available.
Until we have better data I think that it is entirely appropriate to treat all current data from KZ government as intentionally falsified and either apply a reasonable multiplier (historically from other similar cases, a 10x multiplier seems appropriate; certainly that would be a better estimate than accepting their reports at face value, in similar earlier situations the reports always have been intentionally adjusted) or treat the local estimates as the best estimates currently available.