OT: Taking care of bathroom marble and grout

[C40_guy]

The house we bought had a bathroom update done sometime in the past 20 years (I think...)

The floor has large marble tiles and the shower has small tiles. The grout is dingy in places and the tiling darkens a bit after getting wet.

What should I do, if anything, to clean the grout lines and seal the marble against absorbing water?

Is this a DIY or should I outsource. Googling suggests a lot of individual grout line cleaning, brushing, etc...

Thanks!