Ohh ick! My bathroom in the French countryside looked like this when I first moved in (the Swiss taste must have travelled across the border...) Those tile tattoos are worth a punt to cover up the weird ones. notonthehighstreet.com has a big range and they say they are bathroom tested. While you wait to rip it out, I would just paint the ceilings, walls and cabinetry a combo of white and cream (a tone that matches all those tiles). The blue floor tiles might then ping and look pretty good. Lush towels and a good shower curtain (you can get two layered ones that are nice waffleweave on the outside) will help a lot. And you could take the doors off the tall cabinets either side of the sink and have folded towels, attractive decorative bits, and baskets to store the more practical stuff you need in a bathroom. As for those saloon doors....actually, the more I look at them, the funnier they are and I would keep them for a while just for a laugh. I hope they have a good authentic squeak to them :)

We lifted our encaustic tiles and relaid them on a new floor. Most builders will say they can't be relaid as its too much work. We ended up lifting each individual tile ourselves and cleaning off all the grout so that the builder couldn't claim the tiles all cracked when he tried to lift them. It then took him a week to re-lay them but he agreed at the end it was worth it. Stick to your guns, I would either leave the floor or make sure you closely supervise the lifting and cleaning of each individual piece.

Can't find exact match but this looks quite possible, in France? https://www.carreauxmosaic.com/collection-motifs-carreaux-ciment/formes.php This manufacturer makes irregular polygon shapes but is in US. https://leanigel.com/collections/specialty-field-tile Perhaps ask Domus or Baked Tiles if they could put it together as they do some irregular shapes? https://www.specifiedby.com/domus-tiles-ltd/puzzle-porcelain-style https://www.bakedtiles.co.uk/ Where did you find the photograph?

I think you need something calming as you have yellow and teal so you don’t want anything to clash. I wonder if a mid grey like Dulux Chic Shadow would go well? Here’s a couple of pics