Since you do not live in the house yet I suggest you move in and give it a few months. I have many friends and relatives with similar oak in their homes and none plan on changing it. It isn't a big deal to them as long as the spaces function well.

I do have white trim with my oak cabinets and paneled interior doors. The trim was never oak so I did not need to think about painting a good wood. HGTV has been big on showing people hating oak - it's marketing - get people to dislike what the have and they will buy new stuff:)

My trim was dark stained pine which I painted white. It has held up well but I admit repainting the trim on the main level - at least around the doors is on my todo list. It does require a little more upkeep.

Wood moves with changes in heat and temp. This causes hairline cracks in the paint at the joints and this is why most factory white cabinets are MDF or a combo of MDF and wood. The MDF is more stable as to movement and there is less chance of cracks at the joints. For this reason finished wood cabinets that are painted may need a bit more upkeep, or you may have to settle for the little hairline cracks and the durability of the paint is a little less than a factory painted cabinet. Still, paint can help a kitchen with worn or cheaply made cabinets look better or buy time before a remodel can be done.

I painted older kitchen cabinets and moved them to the laundry room. It has been many years and they look OK. I have one painted vanity and 3 wood vanities - the wood ones need much less care - especially if you have children and as I have, dogs - puppies actually who love to try to climb my cabinets:)

If you really want dark gray, then you will want to paint because cool grays and warm woods look drab together. If you love gray, fine, but be warned it has been so over used it is fading in style, though light gray as a neutral will always be a choice. Warm wood tones are returning and you may get your house done at great cost just to find out that gray / white is over. That doesn't matter if you love it.

I put in my oak cabinets many years ago - and I still very much like the warm tone and will do oak again if I ever do a new home - probably a different door style - that is what I mean by liking something even if it is no longer in style. Few can afford the design trends merry go round. One way to stay away from the design merry go round is to go with a timeless style of the past - like craftsman or mission - and do it well.

My kitchen is in a somewhat vintage style:

https://www.houzz.com/photos/my-pics-work-in-progress-phvw-vp~110720042

Here is an example of white trim with stained doors:

This Old House 2016:

Here, wood trim is mixed with lighter cabinets - this wood trim actually replaced a former white trim:

This Old House:

I have a "wood kitchens" idea book which includes some refreshed wood kitchens and you can look through that too.

Some use gel stain over finished wood to darken it. I have heard mixed results on how well that holds up.