if you want old world, I suggest you splurge and use 'old world' materials, namely the cement or terra cotta tiles. those you have pictured are a porcelain knock off.

Lots of pics!

Wanted to show you some other options. instead of using tile on the wall, think about board/batten, plaster, beadboard, nickel gap planks, Wall paper above the wainscot or on the wall behind the sink, etc.

what about your vanity? you could do a solid slab (wall to wall), find a vintage piece, make something, etc.

quick example on the walls. beadboard w/trim and painted wall above. solid wood vanity top going side to side. simple, easy to do all of this, and not expensive. more on this option below.

Now your tile. if it's a small room, and you want a specific look, don't skimp on the floor.

This is the real encaustic tile. tons of colors/designs. this one is the Zebra Terrazzo

For my coffee bar I did the Alhambra cement tile and custom walnut and marble

this would be very busy on floor. what does your space look like? what's your vision for it?

are you going for this look? (this really isn't Old World)

This is the porcelain tile. consider splurging on a better tile.

You could always do a plain white tile on the half wall, or do a nickel gap bead board but this floor tile grabs all the attention.

personally I'd do a black terra cotta mixed w/a zellige or a cement tile

https://www.riadtile.com/product/belgian-black-terracotta-tile-star-cross/

what about this hex tile? is the Aster, on wayfair, it is a porcelain, but it looks pretty good. not as busy as your other

I'd use a white oak vanity w/the black and white. shown in this pic is a white zellige tile.

Go to bedrosians and look at some of their tiles. lots of styles you'd like.

Zia tile, Riad, CleTile,

or, try a black or terra cotta zellige tile in a herringbone on the floor.

I used it on my floor in the pantry area. 2x6 black zellige tiles I found on sale.

if it's too expensive (shipping can get pricey) check bedrosians for some ceramic look alikes.

zellige tile up the half wall . you said you wanted 'old world'

You're going to need some wood and metal

A diff type of old world. wood piece used as vanity, I like the wood ledge.

A real cement tile.

if you want a bit warmer, do something like the tiles above, or an acutal terra cotta tile

check this site too for old stone tile, terra cotta/zellige/cement

https://www.riadtile.com/buy-cement-tile/

I love their tumbled moroccan limestone. this would be stunning on the floor w/a wood vanity and half wall of the star and cross black tiles

https://www.riadtile.com/product/4x12-akal-dark-moroccan-limestone-tumbled-honed/

take an old dresser and make it into your vanity.

i don't know what type of layout you have, but just doing a quick photoshop w/some of the itmes mentioned: soft black board /batten instead of tile, wallpaper above it,

(of course you could do any color you like)

zellige star/cross floor, antique wood vanity, wall mounted faucet, etc.

Becki Owens has done some nice powder rooms w/that a zellige tile: wall and floor.

another old world idea, plaster the walls. Roman or venetian plaster is a pretty simple DIY job. cheaper than doing tile. but you could do half the wall in this and half in the tile. tons of versions.

you could also do one full wall in a cement tile, a console sink, plain floor, and some other older world elements (I might have done pendant lighting here, or did a dark ceiling)

bedrosians Casablanca tile would be a nice choice for that

but, think about doing a slab wood vanity instead of the others shown. can you DIY?

Walnut is beautiful w/black and gold (and terra cotta)

hundreds of ways to do this