Always best to use oil based stains and paints on wood to avoid raising the grain and the timber absorbing water on the working side and causing differential expansion .

You're past the grain raising on that color side , but you should coat the underside with the same amount of coating to prevent unequal absorption of ambient moisture .

It's not going to be a big deal with anything that lives it's life in a conditioned space though .

If you had put a bunch of water-base on one side without those framing members attached , the working face would expand and cause the board to cup , arching the color side upward .

You can use just clearcoat on the underside if you want . Make it the same amount of resin as the top either way so it experiences equal absorption/release  of environmental humidity .

Again  , something like this isn't going to be subjected to environmental extremes .