Previous handle was a pimple on a 2 way screw (no idea what these are called or how it was still holding on) so replaced it with one on 4 bolts on washers for a better grip.
After taking it off it appears that the screw was “sealed” in some sort of wood filler.
Looking at the pictures I think the wood will break before the bolt cuts into the metal.
Yeah the nuts are cutting into the wood. OP would have to do something different to broach.