My experience (not trays)
Generally speaking, there is much more expansion and contraction across the grain in timber than there is in length with the grain (Exceptions do occur though). Different timbers have different expansion/contraction amounts and these are recorded in the texts and can be researched. However, floating panel joinery (which is what you are talking about here) is a pretty well known science. I do not make trays (or not yet anyway as we have too many antique/old trays to need any more) but I do make boxes. The bases are usually veneered ply - almost no change in dimensions with these so fully glued in all around - but the lids (often circa 300 mm x 250 mm in size) are solid timber floating panels. I allow about 1 mm each end and about 1.5 mm along both sides. The sides of the boxes are mitre joined, glued, no splines. No problems so far.
However, if I were using unknown timbers I would either check their expansion/contraction stats or else allow a generous 2 mm each side and 1.5 mm each end. There is no great need to have the dado/groove/slot much wider than the thickness of the timber. You do not want it to rattle around, but a firmish fit is OK (so about .5 mm wider than the edge thickness of your panel say).