Powder/Laundry
since it's a smaller space, maybe it makes sense to paint the wainscoting white and stick with the white cabinets? then could keep the color palette neutral with a light grey or white countertop (would have to do the same in the laundry) and could do a bold color like you want on the walls and the wood-look tile?
long format tile that gets the wood-ish look but is still durable? might be good for downstairs bath/laundry, keeps it neutral and then you can do bright colors on the walls with the wainscoting like you wanted
Q