Prevent sagging shelves in alcove
Assuming that the sag would only be in the middle of the front edge of the shelf you will have to add something stronger than the along the front edge length. A 1x2 on edge (actual size 1.5&quot; vertical and 0.75&quot; thick just is not strong enough to prevent significant sag.
Since you will already have the raw edges of the 0.25&quot; plywood showing along the front edge an added additional piece of wood would hide those edges and trim things up nicely.
For the stronger wood piece I would suggest adding a piece of hardwood like oak such that its upper edge is even with the top plywood. The bigger the vertical dimension that this piece of wood has the stronger it will be. Over a 49.5&quot; length I would, based upon practical experience, suggest that the oak piece be 0.75&quot; thick with a vertical height of  about 3&quot; actual. You would still not want to climb or sit on the shelves but they will sag way way less than your current 1x2.
If you have the plywood cladding installed so that it does not overhang the edge of the 1x2 you can use the yellow colored wood workers glue to secure the oak piece on place. A series of five or six clamps will permit clamping the piece in place. (Recommendation is to not install the lower plywood cladding till after the gluing is complete so that clamping the oak piece to the 1x2 is easy from the lower edge).