Any advice, BM White Dove for the ceiling, walls and trim.

a natural stone tile for the floor.

Wood cabinetry to warm it up a bit, with no natural light in the space.

IMO faux wood tile is dated and honestly I think using fake wood look when it is placed where you would not do real wood is a big mistake. I love dark porcelian 12 x24 tile for bathooms the size you have then a smae size tile same color famity for the rest of the tile needed . I think some a bit darker tile on the wall across from all the dark cabinentry can bring some balance to the space too . Seems you are going very traditional in the space so make sure all your choices work for thta style and for me the dark fixtures would be better on a bit darker larger format tile in the shower

Since you say you have no natural light in this room I would keep it light. You don't have to use Edgecomb Gray in this room just because it is everywhere else. It is not unusual for bathrooms to be a different color than other rooms. Why not use White Dove to keep everything light and bright? In the bathroom below they used a marble (or marble-like porcelain, which is what I would do) mosiac on the bathroom floor. Then you could use a variegated gray tile on the shower floor and use gray grout. I wouldn't use vertical paneling on the walls like they did, but perhaps this picture still gives you something to consider.

White Tile Custom Bath with Tub · More Info

Suggest a different approach in deciding.

Just because EG is used thoughout, I’d wait until the flooring and tiles are chosen, as they are the harder and most important decisions. Bring home samples and lots of paint chips to decide on paint color (are you painting the vanity?) A mood board is the best way to envision an outcome.

If you are set on EG this link may help with complementary colors and undertones.

https://threebearshomestaging.com/2024/05/24/paint-color-review-edgecomb-gray-hc-173/#google_vignette

Given it’s a dark space, I’d use EG on the vanity only. Consider other than white subway on walls and also use on shower floor. Look for a medium color for grout.

^ agree, I would start with flooring and tile choices before paint. Do you have a good independent tile store in your area? the folks that work there are usually very knowledgeable

You haven't even started the process and you're already worrying about wall colors. Wall color is the LAST thing you choose because it's the easiest to change and the choices are in the thousands. I'd start by analyzing the layout. Does it work for you? Are you keeping the tub and shower? If you're worried about a dated look, then that step up to the tub and the raised cabinet on the end of the room scream 1980s. Your inspiration photo shows a free-standing tub, do you have enough room for one? They need space around them which you may not have. Unless you are engaging the services of a bath designer, you need to draw the room to scale before you even think about finishes and colors.