Its beautiful. would not have guessed a red oak

Not oak. Oak doesn't have as fine a grain. Possibly cherry or ash maybe. Not close enough to see the grain well. Stains look different on each type of wood so it would be hard to say what stain. If you are trying to get a match bring a drawer with you to a paint/stain store to get a match.

That looks like it has a white or light gray treatment. It doesn't look like natural wood. You can see the blotchiness in the lower drawers.

You might try contacting the designer. More pics:

https://www.christieadamsdesign.com/blog/2021/9/19/project-reveal-ridgewood-nj-bathroom-transformation

My custom cabinet maker agrees that it is hard to tell from the pic.

The designer was asked about the cabinets and only replied that they were custom made.