More to the point, how much white can I use in the bathroom?

myself I would do wood with the quartz counter top...but if you like the white on white... go for it

IMo bathrooms can be quite different from a kitchen as to finishes but not a completely different style so if you want a white bathroom do it maybe the one upstairs and then keep the one downstairs with the same style cabinets as the kitchen but walls and tiles in white.

My Dad did a white quartz counter top with a stained cabinet and I think it looks nice:

I did white vanity cabinet with marble counter top. The wood element came in as the linen/laundry cabinet. I'm really happy with this but a lot of people discouraged me from having so many different colors going on at the same time. You can have a lot of white and also have warmer/wood elements. Just decide where you want the white and where you want the wood/warm. I don't have a picture, but there are some shelves in a tall niche stained to match the cabinet so there is some tie-in. The shower is light greige field tile on the sides with green/marble/glass linear mosaic on the whole back shower wall.

For the kitchen paint, the colors on my computer screen looks really nice. But if you're not happy with it you could go a little lighter. You're going to have to test colors. Before you do that make sure your light bulbs are changed to LED in a nice bright color. That will help you accurately judge your paint samples.

I forgot to say my house is all "cool" colors. Your house looks mostly like "warm" colors. My Dad's house is warm warm warm, and he was still able to put a lot of white in his bathroom. The thing that tied it all together was a consistent paint color. He used SW Accessible Beige throughout his house. That color is "greige leaning warm" and it worked with the wood floors, white kitchen cabinets, taj mahal counters, alder stained bathroom cabinets, fireplace rock, greige floor tiles, etc. It worked with all of that so if you want to go a little "cooler/whiter" in the bathroom you might be able to tie the whole house together with the perfect greige paint that leans a little to the warm side.