The best option is to have your contractor sand a section of flooring and apply a selection of possible stains to have you approve from.

The color you have now is actually nice (it's not too orange, which some people don't like).

With red oak, you will not get the pale white oak look that is popular right now.

PS. You might want to select different pictures to show the flooring you have. There are nefarious sorts on the internet who like to do things with children's pictures. You can edit your original post to remove them.

The advice about family pics is a good one. I thnk the advice about testing stain also. I like the color you have it works well with the other floors and so maybe walnut color but only you will know when you see the samples

Light stained wood floors have been trending for several years, but it might not be the best stain color to complement your other permanent elements, like Travertine and dark stained cabinets.

I like your current floors. My prediction is that with design trends moving to warmer traditional styles, these warmer medium stained floors will be getting more popular again.

The current pale light oak European Oak, can be something you can get closer to using Bona Red Out two coats of Nordic Seal and coats of Traffic HD Raw. A matte finish. Search Red Out for pics and discussion.

I also like the current color of your red oak floors - a nice medium brown tone that doesn't lean red/pink/orange/etc.

My choice would be to sand them and put a Natural Seal on them.

As others have said, the wood floors are beautiful. They’re a lovely deep brown. I see none of the reddish tones that usually come through with red oak.

Though I prefer one uniform flooring throughout, your floors perfectly coordinate with the travertine floors in the rest of the house.