I make freestanding furniture rather than fitted pieces, so I'll defer to others on the forum who are more experienced than me.
Just to say the spans on your shelves look to be about 900-1000mm wide. If they'll be loaded with books then you really want to be careful about sagging.
Resources like "the sagulator" (really useful by the way),
https://www.woodbin.com/calcs/sagulator/
will suggest that 3mm of sag on these shelves is okay, a tolerance that's widely accepted. But personally I hate any hint of saggy shelves and when I'm making stuff for myself I work to a maximum 1mm sag tolerance. Here are some bookcases and alcove units that I made for my house,
These all have similar shelf spans to your project. Even if you were to use 30mm thick MDF you could only have a light loading of paperbacks before you'd be at the 3mm sag limit, and you'd have no chance of hitting my 1mm sag limit. But I want a maximum of 1mm of sag even with a shelf packed with heavy hardback books (which averages out at about 15- 20Kg per 300mm), and I don't want shelves thicker than 30mm.
Consequently you'll have to either use whopping great lippings front and back made from a stiff hardwood like Beech, or you'll have to use solid softwood or fully 30mm ply, or if you want a lighter construction you can use a hollow core/torsion box principle.
I use plenty of hollow cores for floating shelves. Here for example are some 60mm thick floating shelves I made for my kitchen,
These can be just 6mm Birch ply separated by softwood dividers, they'll weigh nothing yet if designed and made accurately they're phenomenally stiff.
And if you've got the budget you can go even further. A workshop where I was working once made some collectors storage cabinets for a client in the USA, to keep shipping weight down they were made from an aluminium honeycomb composite that was skinned with 3mm MDF then veneered with saw cut 1.2mm veneers. The whole thing weighed nothing but you could have parked a locomotive on it!