Although 10 years old, this article describes and shows a side by side comparison of cleaning a bathroom floor with a commercial cleaning solution and cleaning with baking soda.  I made the mistake of laying down light-colored tiles along with light-colored grout in a bathroom remodel five years ago, and have the same problem of darkening grout.  Let us know at UrinalFly if your quest for clean floors around your toilet involves scrubbing with baking soda.  I can’t wait to try this when I return home.

https://www.wisebread.com/how-baking-soda-took-my-bathroom-from-yuck-to-yes