Butt joints with screws in endgrain is a very weak joint. I would not feel comfortable with heavy shelves secured this way. Screws in the end of plywood are notorious for pulling out.
A pocket screw would be much stronger than a screw stuck straight into the end, but still not great.
Pockets screws with glue would be better.
Dadoing a slot for the shelves to sit in would be ideal, but looking at your design not sure you could work that in.
I would consider adding some kind of mechanical fastener. This could be small L brackets (you could make a slot for it so it doesn't stick out), or small gluing blocks. With little Gluing blocks you can angle them, then paint the outside edges the same color as the shelves. This would still look nice and add a ton of strength.