From your swatches, you’re not afraid of colour, which is great. Now I’m a blue girl, but in this case I’d go for a mossy green. Haymes Chlorophyll or Leek Leaf for example. Saturated colours can soak up light and dry a bit darker in my experience, which is why I’d lean toward a slightly paler, but still solid, tone but if the room is large, bathed in sunshine or you love the moody look, a deeper colour would also work. Do not skip trialling a sample pot though, colour is so site specific. Level of “glossiness” also impacts the look, but paints have evolved so much that you don’t have to go for a shiny finish unless you wish. Do get advice from a reputable retailer about that. Many also have colour consultants or trained staff who can help too (usually free if it’s just a quick question or two)

Everyone has different tastes. IMO the colour that the board is at present goes well with the tile so I'd try and get similar, or same tone but slightly lighter. IMO the orange colours completely clash with the tile. I don't think any bright colours would look right with the tile.

You need to have your samples against the tiles. What look are you after? Do you have any inspiration pics? I like the point above re the existing colour of the mood. Darker for moodier, lighter for more bright.

A soft neutral colour would complement the tiles, then add a splash of colour with your towels.

The bright oranges and greens will definitely look wrong. Love the feather soft colour that Julie has posted, it will add colour but will be timeless.

I’ve just done a bathroom with walnut vanity, chrome fixtures and a similar tile. The feature tile is olive green and it looks fantastic.