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25mm ply is heavy to start with, especially across 2300mm. I used 18mm across about 1200mm and didn't trust it without a central support (so at 600 in from either end). I looked at the sagulator mentioned and probably overbuilt it from there.
The depth of the shelf and what it'll have on it make a difference as well - if it's one paperback deep you might be alright but if it's e.g. vinyl LP depth it might struggle without some intermediate supports which come out to nearly the front edge.
We have a big recess between two fireplaces, like 2300mm wide, that I’d like to fill with bookshelves. Would 25mm plywood sag if I used aluminium supports on each end and a few along the back length? https://www.wickes.co.uk/Alcove-Shelf-Bracket-Black-190mm/p/249884