Skip the backsplash and either
Replace the countertops with something more versatile, with that extra money.
Or

Leave the countertop and do wallpaper instead.

Keep the flooring simple. Brown wood look tile.
Or plain slate tile. Not many options with the countertops. If you change the countertops you can have fun with the flooring

I think this looks like Caravelas gold granite and probably has other names it goes by as well. I do think a wood look tile in a herringbone pattern would be nice as the wood tones look great with this granite. A lighter vanity color in something creamy like SW Alabaster or BM Pale Oak would be pretty and pick up the lighter tones in the stone as the current color is not quite right. A simply creamy off white subway tile in a herringbone above the tub could be interesting or if you plan to redo the shower tile then a classic subway for both areas would keep it classic and serene. A greige on your walls could be warmer than the grey you currently have. It is a pretty stone that is not showing up well with that grey color.

No wood look herringbone with that granite and IMO no gray either flooring should be a close match if not the same as the space I see at the door. As for the tub I need to see that space but first redo that vanity to a cor that actually works with that stone . Or change the counter before doing anything else . It would also be helpful to see your bedroom which appears to be the room next to this. The whole room is also a must . Wood look tile IMO is a dated material but I need more context . Master baths should coordinate with master bedrooms

Ignore tile near vanity, but thought other choices might work with the counter, as well as complement what can be seen in bedroom.

Thank you all so much! I love these ideas and I'm so excited to begin my deep dive on materials (and figure out which ones AREN'T backordered!)