I would fill in the spaces with thin wood (veneer), glued and clamped. The rot ate away some of the inner ply, that needs to be put back. Maple or birch veneer would be a good filler replacement.

Lisa, I use 5 minute epoxy for this type of repair. It not only bonds the wood, but forms a literally indestructible edge that can also be sanded. It is not a really hard repair, but clamps and epoxy will end any future separation as long as you spread it around the affected areas. I can make you a video tutorial if you need it, or see my repair videos on my youtube channel .