I believe the bottom piece is made of Lauan plywood which is a low grade of plywood. On furniture it’s used as the back piece as a dust barrier. It’s usually a little rough, stained and finished with a flat finish. Filler will stain different than the actual wood. As Lee said, it’s essentially hidden from view and I’m sure that’s why a cheaper grade was used. The carcass of the center tray is also made of plywood but a higher grade and then covered in a very thin layer of walnut veneer. Rather than sanding to remove the old finish, I’d use a gentle stripper in order to preserve as much veneer as possible. Once removed, then smooth out with 0000 steel wool, clean with a tack cloth and then stain. Once dry, follow up with a satin finish polyurethane. Any dents or dings won’t show as prominently with satin finish but gloss will highlight them. I didn’t not refinish my wood trim but I have refinished a lot of furniture and this method has always worked for me. The key is to be gentle and don’t get impatient nor aggressive.
