A wide drawer like that would at one time have had a central muntin (H-profile timber piece) fitted from front to back of the drawer to carry two separate drawer bottom pieces. Once a hardboard drawer bottom has been overloaded and deformed, there is no going back.
Your biggest problem is that the drawer sides and back look like they are formed from a single piece of vinyl-wrapped chipboard with folded v-notched corners. On this tyoe of drawer the drawer the sudes and back are folded around the bottom (which is held in a groove). The ends of the drawer sides and the back of the drawer front are drilled (and the back of the drawer front is also grooved), then everything is dowelled and glued together. This process makes repairs difficult as there us no easy way to remove and replace the drawer bottom
I think that if you can find some suitable thin strips of wood it should be possible to glue this across tje bottom of the drawer at the edges and across the middle of the drawer to provide some extra support. I'll put s sketch together to show you what I mean
Ideally you'd want to remove the front and replace that drawer bottom, but trying to pull the drawer fronts off is likely to result in the drawers being destroyed...
