Not sure what was the level of automation on this 125 , but this could also be a ergonomic error in setting the FL in a box or a display of some kind.
Could have been one pilot doing the R/T and the other entering the figures.
so the immediate read back FL200 is correct because done by same individual right after the transmission but if the other enter 020 i.s.o. 200 , and not cross- checked , that could explain the later transmissions : "which level are you climbing to ? : PIC reading the display : FL020 ... ( as in the report page 4 )
Speculating of course.