The thing about paint colors is that a color that looks fantastic in one room looks horrible in another. It all depends on the light. Some very popular grays recommended on here were major duds in my house. A gray with blue undertones we loved in the LR was a definite no in a bedroom on the other side of the house. Grays in particular have undertones, blue, green and brown (the greige colors) being the the biggies. Do you have an accent color going on somewhere? That might be a good undertone to try out. I'd try that "Misty" color that Sophie posted if you're looking for a slightly blue-gray. Depending on how dark or light you want to be, "Sheep's Wool" or "Stonington Gray" might work. Were I you, I'd take a trip to the paint store and pull every color you think is even possible and tape them on your wall. Be sure to choose some colors that are outsiders - too dark, too light, too some probably-not undertone, even a color you hadn't considered like the "Simply White." Look at them in the morning, afternoon, and night. Look at them on a sunny day and a grubby day. Start pulling off the no-goes. When you get it down to a reasonable number of possibles, then buy some sample size cans and preview larger swatches on the actual walls, both in the kitchen and in the adjacent rooms. You might want a lighter version the hallway. You don't want to be like me when I first tackled the LR. The color I thought was "the one" just wasn't when I painted the whole room. Either was my next go. I painted that stupid room 3 times before I got it right! (This is what we finally decided on for the LR that was terrible in BR on the other side of the house.)

BM Stonington or Coventry grays are distinctly blue gray. I totally know what you’re saying about green or purple undertones. If you need something lighter have them mix it at 50% or 75%

Pull the background color from the wallpaper for the first paper This is the background from the second paper but it may be too light. This is the background from the black paper used next to the second wallpaper and this combination works well.

Something light and slightly cool to work with your rug like Sherwin Williams Opaline is what comes to mind. And to look more pulled together consider adding that teal/green tone in accents in the living room (throw, pillows, art).