Additional support for closet rod
One simple thing to try that would not be too much work would be to re-mount the plastic bracket in nearly the same place on the center divider panel as before. Instead of the short screws use some bolts like these:



Select the bolt diameter that will work with the mounting holes in the bracket. Select bolt length sufficient to protrude through the bracket plus the thickness of the shelf side panel plus enough extra to engage the nut.

Drill suitable holes all the way through the side panel of the shelves at the location that you would re-mount the bracket. Clamp on a scrap piece of wood against the opposite side where the drill will come through to prevent chip out of the side panel on that side. Then mount the bracket with the bolts through the holes. On the opposite side apply some flat washers as pictured below on the bolts and then spin on the nuts. Tighten the nuts using a screw driver and wrench or pliers to hold the nuts.