I’d try liberal application of Gorilla Glue, sandwich it in boards and clamp the shit out them. I might put wax paper between the glued surface and the boards and scrape that off later.

that straight groove complicates an easy laminated particle board replacement with some perimeter cuts

Smash it flat with hammer

3D print bracket(s) to hold shelf

Done.

Get a circular drill bit, cut out the damaged parts, use them to template and cut new inserts, glue / secure in the holes.

Like you'd repare a hole in dry wall.

Particle board sucks ass. Looks like a side of a drawer. Going to have to bite the bullet and bust out the table saw and some plywood for starters.