Your limestone floor is beautiful. But isn't this always the problem with white tile floors, whether ceramic or stone? They show everything. I am not aware of any coating that would prevent that, but let's see what others say.

limestone is absorbent and this is why some avoid it on the floor. Make sure it was sealed when installed. You can always reseal. But a few installers told me it needs to be thoroughly cleaned professionally to really maintain the new look.
it is a nice look and feel but with everything there is a downside. I ended up going with a porcelian that feels and looks like a limestone.

If it's any consolation, I have a darkish ceramic floor and I have to clean it constantly. Dogs, kids, life...

Don't feel bad. I have customers who mop every day but cannot get their limestone clean without me coming back to clean it for them. If by mopping you find it cleans well consider yourself lucky.