it’s a common misunderstanding and it’s actually something of an in joke with the fandom. there’s a really good edit someone made that basically changes the canonical order to be:

The Mechanic (2010)

The Mechanic II (2013)

MECHANIC III: New Dawn (2022)

The Mechanic 3 (2015)

MECHANIC 2 (2020)

MECHANIC (2019)

The Mechanic: Revelations (2014)

which works remarkably well. they actually brought back the original director from the first two the mechanic movies for new dawn, so stylistically it fits better even though it was made a decade later. the end result is a sort of rashomon version of the mechanic narrative. it’s really a must watch for mechanic fans.