it might just be the lighting, but the paint on your wall seems to have a peach tone. I would consider painting the walls a warm white or perhaps do a removable wallpaper. I would not recommend painting the tile. The tile also looks to be in good condition. I would decorate around it.

You could also do a light pastel blue on the walls.

You'll gain nothing from painting the tiles other than cheapen the space; let them be. Choose colorful accessories for the bathroom as a stop gap til you are ready to redo.

Deep clean the grout, tiles and tub, new caulk on tub, fresh paint on walls, but don't paint tiles. I

I find it interesting that in a lot of the remodeling jobs I am seeing on HGTV, 4” and 6” square tiles are being used! So, I don’t think your tiles look dated at all. As has been suggested....look into repainting the room, changing out hardware and accessories. And find a fabulous shower curtain! Leave your shower and tub alone. They look fine!