I would get a piece of that slate and test out a few things to see how porous it is. Drip bleach on it and other chemicals you use that might lighten or etch it. Nothing worse than setting down a toilet cleanser and leaving a ring on the natural stone.

Not to worried about the slate in the bathroom. I don’t use bleach (we have septic) or harsh cleaners. Also plan to seal yearly.

My master bath is similar to what you're talking about. I used a slate look porcelain on the floor and a varigated (shades of gray) 2" hex on the shower floor. I used real Carrara marble on the countertop and sills of the shower (where the glass meets the curb).

I'd be tempted to leave the white in favor of a light gray with a bit of a stone-ish texture. Then you could use a smaller version of the same tile for the floor. Maybe something in a pseudo-concrete instead of a pseudo-marble?

Try this hex, it has a matte finish that works well to the floor and it'll look great with the wall tiles.

https://somertile.com/ProductDetail/FRGLVXDG_Liverpool-Hex-Dark-Grey-1038x1138-Ceramic-Mosaic

I would not mix slate and marble in the same space but I also do not like subway tile in showers , a 12 24 porcelain tile in a color from the slate and that same color smaller tile for shower floors IMO a better choice. I use slate outside for outdoor kitchens in Canada no issues , pretty sure it will be fine in the bathroom. My aim in bathrooms is as few grout lines as possible and I aslo think hex tiles have been overdone .

Cautionary tale, i deeply regret putting marble hex in my shower. Looked amazing initially and now after just a year it doesnt. We squeegee after every shower and it doesnt matter, the stain is irreparable.

Thanks for sharing! Yeah I just love everything marble but I know I’ll be disappointed if it turned yellow on me. Yours doesn’t look bad though.
I’ve decided on a gray penny tile which also has its difficulties since it has so much grout, but it’s the only thing I liked other than marble 🤷‍♀️