Well thats where i get nervous. In all honesty, I’m not sure the guy who installed our floors knows about stain colors. He’s part of my contractors team of workers.

Ask for white wash finish in hard wax oil or water base matte finish to achieve the look you want. Your floor guy should know this. If not, they do not have enough experience.

Do you want a urethane finish with some water resistance that you can use a water based cleaner on, or an oil finish that's more easily renewed without recoating large areas periodically?

For the first you'd use either a Bona DriFast White stain and a non-yellowing urethane like Traffic, or substitute Bona NordicSeal for the white penetrating stain.

For the second you'd use an oil like Rubio, Woca, Osmo etc.

You need to see smaples of how they will deliver what you want .If you do not like what they show you tell the contractor you will get someone else to do the floors. The sample you show are done as mentioned probably a whitewash before a the final finish and make sure that final finish is non yellowing Make sure you get the samples and sign off on the exct stuff used for the samples

So I had them do two samples. The one on the left is 2 coats of a finish with a bit of white, but to me it looks darker. The one on the right is one coat of Berger Siedel natural white but it looks WAY too grey (with almost a blue undertone).

Feeling very defeated!

You may want to do a few more samples to find the one you like the most.

My "Floor Guys" are not designers and in fact I had to battle with them a bit to get the color I wanted when I first worked with them. They know wood but not design. It took a while for them to understand what I wanted and for them to achieve it. I trust them but it took some time.

You may need to Bleach the floors or rather have the floors guys put Oxalic solution on them to get them to turn light

But before you do that, maybe some floor folks will chime in. And research everything you can to learn all you can, here is a great blog about oak wood floors and stains options.

Our White Oak Floors: The Natural Finish/Stain Decision by Meg Leonard

Houzz How to achieve natural oak floors

Bleaching red oak hardwood floors Houzz post

I had an expert in floor finishing do the Rubio Monocoat in white on my white oak floors. Four years in and I still love my floors. We are outside Chicago. Look up Naperville Hardwood. He has a great blog on website about floor finishes.

Is this engineered European Oak, quercus robur. Or domestic White Oak, quercus alba? Is it solid? Two different species with different tone and grain openness. Domestic has more open grain that can turn dark unless it's filled.

Ciranova has two products that may help. ECOFIX PLUS (ciranovastore.com)

and WOODLOOK PLUS (ciranovastore.com)

Ciranova is a part of 95 year old French Blanchon Group. Call them for technical support.

Perhaps Bona NaturalSeal + Bona Mega Extra Matte.