Have you checked that the screw was not located into a short piece of small section wood
that was longer than the hole plus an inch or so either side?
Such a piece of wood with a loop of string to pull it down to allow the fixing screw to locate
might have been how an electrician originally fitted that ceiling rose.
That sounds like a great idea - but no, nothing like that here. There was one long wood screw that disappeared into the hole (where plaster may have been once), and one plasterboard screw in the plaster.
It's probably the best way to solve your problem. Sometimes it's tricky, maybe drill a pilot hole in the wood although it's a trick to line it up with the screwhole. If you go to thin or short on the piece of wood it will spilt.
Have you checked that the screw was not located into a short piece of small section wood
that was longer than the hole plus an inch or so either side?
Such a piece of wood with a loop of string to pull it down to allow the fixing screw to locate
might have been how an electrician originally fitted that ceiling rose.