Oh my. Oh my.

It's wall tile so it's not going to take a lot of abuse like floor or shower tile. Maybe you could do this. I would do an off white you pick from the floor tile. https://www.google.com/search?q=how+to+paint+bathroom+wall+tile&rlz=1CAYBVP_enUS893&oq=how+to+paint+bathroom+wall+tile&aqs=chrome..69i57j0l7.5466j0j8&sourceid=chrome&ie=UTF-8#kpvalbx=_-TWOXtnFFYHv_QbSqobQAQ48

There is tub and tile epoxy. I erased my chocolate brown tub with that as temporary fix but it has held up for over 15 years. stinky and messy but so worth it. Professional refinishing can give more color options than the just white I used.

Are you talking about the rusto epoxy?

So much depends on your budget, but if painting is what you can do, then Yes. Paint the vanity white, as well as the mirror and walls above the tile. Then get a few robin’s egg blue towels to go with your new shower curtain and use a large, washable, rectangular white cotton rug. Done, until you can redo the bathroom.