Plywood can be a design feature on high end cabinets. We had cabinets made for our kitchen remodel by a company called Henrybuilt in Seattle. They made the plies on the wood a design feature.
We love them. Wish I had a source for this quality of plywood. We visited their manufacturing facility one, it was very impressive.
Bob
You have two options for sourcing the plywood.
The first is to ask the company that made your drawer boxes where they buy their plywood.
The second is to go to a quality woodyard not a big box store and they can supply any quality of plywood that you want to spend the money on. The only problem is that they will stock in large quantities so you won’t be able to make a specialist order fo a couple of sheets.
However they will certainly be able to tell you the woodyard which carry the kind of plywood that you want all that can order it in. They may also be able to tell you the retailers that they sell to. Plywood in an 8 x 4 sheet can cost anything from $30 up to several Hundred dollars per sheet if you’re getting a complete hardwood veneer with hardwood core and a very specialist kind of hardwood made into the plywood that you want to buy.
Shannon Rodgers who makes the Shannon‘s Lumber Industry Update podcast has a couple on exactly that subject.
He works for a lumber company and has very interesting points.