Is the wainscoting painted or finished already? Is the shower tile installed? Has new lighting been installed?

Wainscotting will be painted. new lighting not installed yet. that is the current shower tile that will stay

I suggest priming the walls with white primer, including the wainscoting. Then install the lighting. Once that is done, new wall paint samples can be tested. Matching new wall paint to the shower tile's off white color would allow the showy new checkerboard tile to be the star of the show.

Looks great, so far!

I'd use SW Alabaster for the wainscoting and trims too, just a different sheen.

Walls in Egg Shell, the wood a satin finish or semi gloss. It will show a nice subtle difference.

Just wanted to say the floor looks awesome!

Suggest testing lots of colors, as it’s important the tile is complemented.

Consider all of the bathroom‘s components and then choose paint (I’d only use one color). If too plain, it’s an easy job to repaint lower half.

If budget permitted, consider more modern, streamlined cabinet panels (which will also improve access).

I think a color from the tile would be logical even a bit toned down but still goes with the tile . Not beige from what I see.