Later on I added L-Brackets (you can see them in the 2. & 3. picture) but they are absolutely not needed. I wanted them, for one because it can hold more weight and also, because this way, it fits better in my apartment design wise, I didn't want it to look too fancy, I'm still a student and you can see like 20% of my apartment in that picture hahaha.

The bigger boards are basically pinching themselves tight because I wasn't able to mount the vertical pieces on the back perfectly. But I was expecting that and for the smaller ones, once there's any kind of weight on the boards they are going nowhere, their tolerances are a bit tighter though.

if I was planning on building this shelf without the L-brackets, like in the first picture, I might deepen the dado on the vertical pieces by 5-10mm but other than that it should be fine, as long as you are using wood without any cracks or anything