I fixed it for you.
I cut out the damaged wood and very carefully cut another scarf joint about 3:1 L/W ratio. I used a "Fein Multimaster' with very fine teeth on the blade to make the 'cuts, then 'shaved' the ends with a super sharp chisel so there would be no 'gaps'.
I replaced with entirely new wood, used recorcinol glue and then screwed it to the old, then bunged the countersunk screw holes.
Good as new.
It wont come apart as do 'glue only' repairs.