Hello Steiny, welcome!
A loose, floating frame would be a good choice. Here’s a photo of a 3D chessboard I made a couple of years ago. It was also going to a different climate zone so I wanted something to help hold it together through any possible movement but I wanted a really clean, modern look for this one so I opted not to add a visible frame. I also decided it looked overly chunky from the side and I thought it’d look better if it “floated” a bit above the table so I added a 1/2” thick solid base under it that was 3/4” smaller than the chessboard on all sides. I painted the edges of the base board flat black so it couldn't be seen at all. I drilled countersunk, slightly oversized holes in the base board that would be centered on each of the squares in the perimeter of chessboard and inserted screws that could move around a bit in those holes. I applied a layer of black felt to the bottom to make a nice, soft base and hide the screws. By all reports the chessboard’s still in one solid piece.
View attachment 3925021
Weirdly, I can’t find any photos that really show the base or how the board looks from the side (it just looked cooler from the top so I guess I didn’t bother), but if you zoom in you can see how the sides kind of float above the countertop it’s sitting on.
Jack