I see that the deck around your tub is wood? You are not concerned about splashing on that?? If you aren’t, then I would simply curb with the baseboard wood trim that you are using around the floor. Are you painting the wood trim around the tub or doors? If you are, you could substitute a non-wood product cut to emulate your trim boards, but if you are leaving them natural wood, then I would go with that. I see no reason for a backsplash if you are leaving your tub deck natural wood.

Technically you can put a waterproofing paint over the wall. But it’s not a long term solution. Can probably last 1/2 years and then need to be redone. Why not do tiles? Why don’t you like that idea?

You could install wood on the wall and then use a marine varnish to waterproof it.

Another option would dimly be a curb of your countertop solid surface. Simple.