I built a set of serving trays similar to what you are building.
I reinforced the corners with a spline (ebony) of contrasting wood ( to walnut). I made a simple jig to hold the trays at the right angle. The jig ran against the table saw fence. I used a flat bottom cutting saw blade to cut slots on the corners. I then glued in the splines and, after drying, cut the splines flush with a flush cutting Japanese saw.
If you use a standard saw blade on the table saw to cut the slots for the splines, there will be a small gap under the spline.