Lots of warm white and cream colors that would keep it bright and not stark. Your trim color would be a good place to start.

Was the architect/builder also known as Donald Joseph Scholtz? Here's a link to many photos of his houses. https://www.ncmodernist.org/scholz.htm

One of the characteristics of ranch style contemporary houses built in the late 1950's-1970s was their flexibility with respect to family living. Adding windows and skylights allowed customizing. The color palettes were changeable, too.

All going to say that the house doesn't have to stay dark, you can change it to fit your preferences. Solatubes cost a few hundred dollars to install and provide lots of natural light.

Once the bathrooms are at the painting stage, prime with white primer, install new lighting, and then decide what color you want. As @chispa says, many warm white and cream colors will go well with the beautiful wood in your house.

Here's an excellent article on choosing new paint to go with wood:

https://www.houzz.com/magazine/11-terrific-paint-color-matches-for-wood-details-stsetivw-vs~9025200

Although the bathroom seems to be demolished, can you post a picture or at least give dimension for some context to your request.

Yes. I will send dimensions. No natural light in either bathroom.

Dimensions from contractors and another picture. No natural light.

Do you have any inspiration pics? Idea of what you need or want in the bathrooms? Same layout? What can move and what cannot? Budget?