The stairs should be considered part of the 'public' areas. That means they should match/compliment the downstairs area (the place with the entrance, the living/dining space, etc) where guests come in and move around. Traditionally 'upstairs' would mean private space such as bedrooms. The upstairs areas are welcome to have different flooring from downstairs. That's not a problem. You are welcome to work with treads that are 2-3 steps darker than your downstairs flooring and then paint the risers. This is a very handsome look that will show off both the stairs and the down stairs flooring. If you are lucky, you will be able to pick a stain/finish that is complimentary to BOTH floor colours. Of course, a stairway that has been designed for carpet has a different set up than one designed for rigid flooring. You will need to be careful with how the finishing carpenter finishes the stairs.

I can't see the condition of the tiles or if they're ceramic. Their color would work with the color you're seeking for the LVT wood planks. If you want the cohesive look of the new tile throughout, I agree with Patricia.

You can mix colors together for a custom match. I would add a little ebony filler to white oak filler.

Our living room needs to be repainted, but has vaulted ceilings and connects to the foyer and hall (the staircase is painted the same color too). I'm thinking SW Pure White like other areas of the house, but I'm not sure. I also need to replace the old, dirty carpet on the stairs and floor, but I have no idea what to put in. We do not want to raise the floor and continue the hardwood, so I am looking for different suggestions.