I used to have those white washed oak cabinets. They were solid.

I would NOT try and stain. Staining those is just as much, if not more, work than painting.

I'm going to pass on a bunch of info and pictures for you to consider.

BTW, are you redoing the floor at any point? the color will figure in to that.

I happen to like your backsplash. I think it works fine. Once you get a diff flooring, it will look better.

What I would suggest to you if you paint (and I think you should) is to add some wood trim to your island to give it more of a finished look.

Here's a before and after so you know what I'm referring too.

This makes a huge difference. diff ways to do it. If you search "DIY wood trim on kitchen island" you should see some ideas.

A few other visuals for you.

Also, you need some hardware. hardware is like jewelry for cabinets. Pick something out so that the holes can be drilled before painting (if possible)

I like these type of handles. order some (that are returnable) so you can see how the size works. you want the handle to be between 6-7" (not the hole spread, the actual handle length) because you do have taller cabinets.

Have you gotten any estimates for painting? You don't have a ton of cabinets, but I would guess you're going to be in the 5K range.

Very important you find out the steps for painting. (You want a pro cabinet painter, not some random house painter).

The steps are:

Removal of doors/drawers to take back to their shop. (marking the spots where they go so they don't mix them up) sanding all surfaces, priming all surfaces, sanding again (to get the primer coat smooth) and at least 2 coats, sprayed.

What's left behind should all be covered and taped off like this so that they can spray. a plastic sheet was put across the kitchen so that overspray (and there really isn't any) didn't mess up the rest of the house)

I can't stress enough how important the steps of sanding, priming and sanding again are. If they tell you they only prime and paint, you will have chipping and peeling. All the grease and grime and the previous top coat that's on there, has to be removed if you want proper adhesion.

Mine were done w/a pre-cat lacquer in a BM paint color

before:

I ended up going w/refacing since my drawers were two diff types. I wanted everything to match. I did the Shaker reface w/a beveled inner trim (for easier clean up)

The price to have these refaced was another 2K which wasn't bad considering all of the new doors and drawers I got. And they built me those 2 large drawers in my island, removed all the dated rope trim/corbels, did the new vent hood, and a few other things.

Do you see how my cabinet doors come down to the bottom trim portion and yours have a 1-2" gap up from the bottom? it would be nice if your doors closed over that completely.

they messed up and gave me doors like yours are now. see how the bottom portion doesn't cover the bottom wood piece?

They had to reorder the correct doors. See the diff?

I'm telling you this in case you have the opportunity to reface. having MDF center panels w/solid wood rails (on the doors) are better for painting than having a wood center panel. wood expands and contracts and those center panels could crack. the MDF won't. The ones I got are all solid maple, with only the center panel in the MDF.

Again, just some info for you.

I like the soft brushed gold hardware w/your colors. If you must do a darker gray on the island, make sure you pick a gray that has yellow or red undertones. NOT a blue/gray.

I can give you more paint colors in my next comment if you like, but just let me know what you think of any of the things I've pointed out to you.

This is a golden granite w/similar tones to what you have. (Except your granite has hints of rose/pink. you may be able to go w/a rose/gold hardware. grab a sample of one)

In fact, these 3 colors appear to be a perfect match to your stone. Aesthetic White leans a little toward the red side (pink) which is the undertone of a white that you want.

And, I think this color pallete would be gorgeous in your room. here are some rose gold hardware choices.

some other colors w/a white cabinet, your granite and rose gold/acrylic hardware.

I'd get some paint samples of a few of these. any of the tops ones may work for the island if you want a paler gray color. And the whites that are listed are warmer, creamier whites.

You'll have to see how they look w/your lighting and your floor. ( I really hope you're going to do some diff tiles down the road. a larger format tile would look so much better since those smaller squares and large grout lines compete w/the counter/tile splash)