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I used 18mm birch ply with full depth (standard) brackets at not more than 600mm spacing. In my case that was one at each end plus one in the middle.
Across 2.4m I'd reckon 24mm will flex under it's own weight. Your rear edge brackets will limit that but i'd worry the front edge could sag in the middle once loaded. If not immediatly then later.
Haha ffs of course this exists! Will give it a try, but in the meantime if anyone else has first hand experience of using ply for bookshelves let me know.