I took the white subway tiles and our porcelain floor tiles and propped them up to get a idea. Don't know why I didn't think of that before. Our floors are not in yet, so it was a bit hard to visualize. We are using quartz for our thresholds and shower jambs, so in our bathroom, the porcelain tiles for the floor look better. Thanks everyone for your feedback, much appreciated :)

I would go with the smallest dimension of tile so it can hug the curve of the barrel vault best. Stay with white.

At first blush, it looks to be a green soapstone-like material in a 4" or 5" hexagon. I did find the following Danish tile that looks very much like it: https://www.mosaikhjornet.dk/produkt-kategori/fliser-og-klinker/vaegfliser/tisvilde/ This one is from Great Britain: file:///D:/Downloads/NEW_TERRACOTTA_DWT_Ceramic_Design.pdf With a more glossy finish, out of Minneapolis, MN: https://mercurymosaics.com/products/large-hexagon-1036w-bluegrass Another possibility with a sales office in San Francisco: https://www.moorishtiles.com/teal-blue-hexagon-tile.html Good luck - you have good taste!

Use a gel foam bleach cleaner. Its not going in your septic system, if you scrub your floors, unless you dump the dirty water down the drain. Once it is nice and clean, have it sealed, so its easier to clean.