I found a thread on GW that has a picture of a white octagonal mosaic with burgundy accents, scroll down until you see the picture. I think you are going to need to incorporate some of the elements already in the bathroom, and the tile trim color seems the most logical to carry through to the floor either with an accent in burgundy, or if you could find a burgundy floor tile- tile the entire floor with it. Here is a link that might be useful: octagonal tile with burgundy trim

10 to 1 the tub is white. I have the very same tub. I love it because modern tubs aren't as comfortable, AND don't have that nice wide shelf for sitting, holding a drink, book, etc. Those are great lounging tubs. Mine doesn't have a liner, but is getting to the point of needing refaced. You can replace that faucet, shower mechanism easily if there's access in the wall behind the tub. Mine accesses through a closet in the adjoining bedroom. I think I'd ditch the wallpaper first, then look at colors. It's so busy it gets in the way of really seeing what you want. I think a gray/silver on the walls to match the tile might work. That vanity under the sink looks like it was added later, and I'd surely get rid of it because of the shape it's in. Plus, it looks like you have heater/vent? next to it on one side. That limits what type of vanity you could go with. Another wall mount of some sort would work if you can't repair the faucet. A good plumber who knows his stuff, and who has done tons of repairs should be able to replace the faucet, or repair it to where it will work. There might be a problem though finding the parts. Is there a storage cabinet at the end of the tub? My bathroom has a big storage, built in so if you have one, you don't necessarily need storage under the sink. I also like the idea of silver towels and other accessories, IF you can match the tile. That is lovely tile, and newer tile just isn't the same quality. Floor-I love it, but replacing with a bigger, maybe silver tile, would make the bath look less busy. Is that an option? I agree with the person who said colored fixtures might work here. I think silver/gray would give an overall finished look.

Pretty! I am doing a similar tile in my bathroom remodel right now. Are you only open to Sherwin Williams? Because Benjamin Moore has some beautiful gray bathroom colors, better than SW in my opinion. I’ve done a lot of research and made a lot of mistakes lol. Here is a good article. I’m doing gray owl, myself. https://www.kylieminteriors.ca/the-9-best-benjamin-moore-paint-colors-grays-including-undertones/

3 lights [total of 6] look nice over 1 large mirror. 19.7 x 3.5 x 4.3 inches https://www.amazon.com/dp/B081YVS5KW/ref=sspa_dk_detail_1?pd_rd_i=B07T62FTHQ&pd_rd_w=jivH0&pf_rd_p=cbc856ed-1371-4f23-b89d-d3fb30edf66d&pd_rd_wg=Bfk0H&pf_rd_r=WWEDZHE85J50VQJ78X3Y&pd_rd_r=be7787a9-e79d-495f-b431-2dddb0f32d0a&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUFOWjhIUzY0SU9UUjgmZW5jcnlwdGVkSWQ9QTA1NzE1NDExVzdQRlFMMTRDTkFWJmVuY3J5cHRlZEFkSWQ9QTAzMzk0MzMxSllSU01XS1kzUlREJndpZGdldE5hbWU9c3BfZGV0YWlsX3RoZW1hdGljJmFjdGlvbj1jbGlja1JlZGlyZWN0JmRvTm90TG9nQ2xpY2s9dHJ1ZQ&th=1