These vaults cause a lot of trouble. Yes, you can paint it all the same. I've done that and there are pros and cons. Pros - lessens the "vault" as a feature. Brings the ceiling down. Softens the transition. This is especially true if there are no architectural elements - just a vast expanse of sheetrock. Cons - the ceiling will appear darker throughout the day depending on lighting and cloud cover. In a gray color, this can be depressing.

From your description I would advise you not to paint the walls white. White needs light to come to life and becomes drab when you don't have enough light. With the flooring you selected I would stick with the taupe colors for your walls. Taupe can be tricky. I have found that many of the taupe colors in both SW and BM tend to either be too gray or have too much purple. The nicest taupe I have found is by C2. You can order samples and paint from the company if you don't have a C2 store in your area. Test the color Filament and Archival. The first BM color I would test would be Pale Oak. It is a bit more gray than the C2 colors, but is a light taupe. I would paint the ceilings the same color as the walls.and would use white for the trim. The white should be the same hue and the white counter. Please test paint colors using large samples. I like to paint my samples on 140 lb watercolor paper - it simulates walls pretty well. Spraying paint creates a slightly lighter color and colors look lighter when they are on a perfectly smooth surface. Most pre-painted samples that you can buy are sprayed and on slick paper. Michaels, Hobby Lobby and Amazon have watercolor paper in a variety of sizes. For neutrals and whites I like the larger sheets (18x24). https://www.amazon.com/gp/product/B00NQ49PLM/ref=ppx_yo_dt_b_asin_title_o08_s01?ie=UTF8&th=1

"Usually, the paint for a bedroom is not selected until the bedding has been selected so" and if you change your bedding often? Sounds inconveniently traditional. You could paint the walls at full strength and go 25-50% saturation of the same color on the ceiling so it feels cohesive. You could pick a color on the same color strip or in the same color area. Try this article The Trouble With A North-Facing Room it lists your paint choice as an option. I think it's more modern to go with the same color and you could make it work with the high ceilings to alleviate the feeling of a cave. Have fun please - no white ceilings :)

My husband and I recently painted the entire interior of our “Forever Home” with Home Depot’s Behr Ultra Scuff Defense Primer and Paint; color: off white. Matte for ceilings and walls; satin for doors and moldings. We even received a 10% military discount from Home Depot, as I am a retired US Air Force Captain. The key to a great paint job is the prep work: we fixed all nail pops and cracks, sanded and primed all areas; then prior to painting , we washed and rinsed all ceilings, walls, doors, and moldings. When we were tired we took long breaks. This paint is easy to spply, no odor, no issues. Every one loves our white walls, and the walls look great all times of the day too! I’ve used BM and SW paint in the past, and like the Behr better! Best of luck in your paint journey.