that looks fine, bench space is where I spread out on (real estate wise) elbow room..It is right around 40" wide (20" deep) I made it to fit that space. Each shelf is framed 2x4s. I did consider the center cross but felt the span wasn't long enough to bother.
There is no racking at all right to left (or front to back) the unit is totally solid as those dados you see are exact measurements of the 2x4. The screws just hold it together the stand is solid wood from top to bottom and no bolts are in sheer. I used to build aquarium stands and used the same general design with wood supporting the load 100%.
The below is the reloading bench I just completed and I am kind of thinking I should have planned on the reloading bench in the alcove space and the ammo shelves along the side.
View attachment 371473
For sure.Those shelves look pretty sturdy... I'd estimate you are only at about 25% of load capacity... load them up. I've got cheap press board bookshelves carrying more weight than that.
Relax.Speaking as a plumber...please please please do not store your ammo under a sink.