The whiteners in toothpaste will leave permanent “drips” on your shirt if you are not careful, too.

My impulse is to try something to darken or deepen the tile color, like wax or buffing with oil. I don’t remember having this trouble before the super-white teeth craze we have had the last couple of decades. I am no stone expert, though. I wonder if there are something like the ”stain sticks” for wood available for stone? Maybe a waxy pencil in various slate colors? I would dab on and wipe off to see if it makes it worse or better. Change the color in small steps at first.

Again, I know nothing about stone! Maybe there is a poultice that will help?

I just know how toothpaste fades colors. You need lessons in standing over the sink for your family members! If you have glazed tile in one bathroom, you could designate that the tooth-brushing room if they insist on dancing while brushing.