Does the tile predate the floor and vanity? The tile looks mid-century, while the other elements look much more recent. And I don't think they particularly play well together. Normally I'm all for keeping and working with mid-century tile, but I think that ship has already sailed in this bathroom. So yes, take out the tile. Shiplap, however...shiplap has been soooooooo popular in every kind of house, including ones that are stylistically unsuited to it, and when you have a trend like that it often means that when it goes out, it goes out hard. Like Tuscan kitchen from the 90s, or shag rugs from the 70s. People make fun of them. That's shiplap 5 years from now, if not sooner. You could just do drywall from floor to ceiling everywhere but the shower.

"...All these photos of interiors & exteriors are what brought me to Houzz when I wanted to create better living spaces in my own home..." Yes, of course. But the problem with many of these posts from folks who throw a lot of photos of one thing or another into the conversation is that they don't generally analyze what and why they post the images. It's just a bunch of snapshots without any real reasoning of why some of the photos might be a good idea, or why they might be a bad idea. The result? Like HGTV, some folks get really excited about the Chinese antique elephant tusk table and go no further in their thinking. It's the difference between architecture and decoration.

Your room seems to be coming together quite well. I hope you're still going to replace the ceiling fan. Here are some rug and pillow suggestions that will add more color to your room. A neutral rug would also work well in your room if you'd like to keep things more monotone. I also think a black/ dark grey rug would work well in this room. It keeps it neutral and yet brings in the required contrast. You could try out a plethora of options for you room like this in interactive 3D here. This is a mock up of your room and can help you make informed design decisions. Do let me know if you like them or if you have any rug that you are eyeing online and i can show you how it would look in your room.

Your Turkish rug is marvelous! Really, any type of modern manufactured rug will look like junk compared to it. Why not just buy more low pile Turkish or Caucasus or kilims? You can find them very inexpensively nowadays, and if you think carefully about where you are going to place them, it won't matter if they have some damage, e.g. wear in certain places, abrash, etc. For example, if where you are going to place it will be partially under furniture, if the part of the rug that is going to be under furniture has a little stain, or has fringe loss, or pile loss, who cares? No one will see it. Or if you will get a long narrow rug for a hallway that is usually dimly lit anyway, who cares if there is some not severe abrash in some areas? No one will notice that anyway. Prices are very good on Persians, etc, please look around, you will be pleasantly surprised. And no, I am not a dealer.