If you only removed the wallpaper border and valance the room would be fresh and more modern. Yes paint. To me putting up wallpaper is easier than hunting for artwork to put on the walls. I am not someone who chases trends. The floor looks like off white tile in good condition. The shower glass looks 'just fine' to me too. You willl have to decide about replaicng the floor because once the vanity is changed you do not want to re do the floor. The shower can be changed later. Is the lighting bright enough? Do you want a different shower head or several?

These two elements stood out to me as well (wallpaper up top and the curtain). Depending on space around the new vanity, half wall to hide the toilet could be nice? But the paint, tile and simple shower doors all look good to me. If you have a different aesthetic in mind, perhaps you could share some pictures?