Regarding the question, yes, from the photo it looks more like artificial wood than real wood veneer. But you can tell if you lightly sand it. Let's assume it's plastic. Then please clean it properly with soapy water, degrease with spirit. Light sanding, around 120 grit or a bit finer, dust off well, apply alkyd resin varnish of your choice, preferably semi-matte, high gloss doesn't forgive mistakes. Use a mohair roller, take the one made of short-haired teddy plush, roll over. If it’s white, one coat should be enough. Why alkyd resin varnish? Because you can thin it slightly with universal thinner, then it levels out perfectly and even as a layman you get a nice smooth surface. Acrylic water-based paints do harden and don't emit fumes, but they level poorly. The result is often not so smooth, like orange peel for example.