" We tried Restore A Finish but it didn’t work. "

Be careful that stuff is awful. Hopefully now you can do something still as that type stuff typically ruins the surface for just about anything else, including paint sticking. What do you mean by Minwax, as they are a stain (either gel or wiping)?

I think the best is to get a good wood cabinet cleaner first and it will remove the years of greaase and dirty hands form the cabinets then do agood quaity wood refresher .What did not work with the product you used ? Did you flollow th instruction carefully . I find most wood cabinets can look like new with the proper way to deal with what you want. I think your cabinets look pretty good they are not a dated style really. Maybe strip them and restain with a different color . I hesitate to advise painting cabinets DIY I have never seen a DIY paint job on cabinets that lasted and most when seen close up are not good. The prep is so time consuming and you need to spary a finish so that means somwhere with no dust no air movement either . Refinishing wood is a much better idea for DIY and still require the same prep but IMO you cabinets are nice as woo. Change all your light bulbs to LED 4000K to start and see how much brighter your kitchen will instantly be .

You would need to thoroughly sand , degloss, degrease, and use a heavy bodied gel stain, which is lets some grain show but is more opaque. If you chose a darker color, you wouldnt have to remove all the existing stain to get even color.... the new darker color would just conceal everything. Or maybe pay to have someone dip strip all the doors and panels.

Minwax isnt the greatest - though they do have some interesting colors now. General Finishes or even Varathane is better. It needs to be aforementioned heavier bodied stain that sits on the surface more and not a penetrating stains, which need to go on either new unfinished wood, or old wood that has every last bit of old finish removed so the stain can penetrate evenly. This being oak, the old finish (prob some form of plastic) has likely gone so deep into the pores of the wood you'll never get it out - hence advice for heavy bodied stain.

Usually Im in the save the wood camp, and while I would never dissuade someone from taking a stab at refinishing wood, I think this would be a huge job and materials to do it arent cheap either.... youd have to decide if its worth it vs say just replacing doors if not entire kitchen. Just doing the lowers might make it more manageable though.....

Alternatively, you could paint uppers the wall color and then a COLOR for your lowers - maybe some version of blue....navy, blue-black, blue-gray? Since you seem to have some blue going on there.... Whatever you do get some new jazzier pulls for the cabinets!

From your photos, I don't see any major finish issues.

If you just want to freshen the finish, try this article by N-Hance..

If you want to paint over the existing finish, largely the same process applies. But, I should warn you that oak is ring porous wood, not a paint grade wood like birch, and when painted over looks like oak painted over.

If you like your kitchen layout, then for a whole new look, buy just doors and drawer fronts from a company like Arkansas Wood Doors.

Please show some close-ups of a worn drawer front and a worn door.

I should warn you that oak is ring porous wood, not a paint grade wood like birch, and when painted over looks like oak painted over.

Ring-porous vs. diffuse-porous hasn't been a significant issue for coatings since we moved away from the old lacquers. You rarely even hear about the texture of the wood changing the coating process anymore.

If you want the grain showing then the ring-porous wood is a positive and if you don't want the grain showing, then you are going to have to apply a grain filler anyway which will mitigate any concerns about it.

What about shellac? I’m not an expert at all but we used it on some old cabinets before and it looked nice. I’m not sure about the longevity. Maybe a feed n wax type of product used for old hardwood floors?

I love your cabinets!

First clean with Murphy’s oil soap. That May clean them right up.

I love the idea of painting just the upper cabinets. That would be beautiful. You could also go with a larger rug that covers more of the kitchen floor area. I like a mixture of lighting types so I’d also suggest a pretty ceiling fixture to go along with your recessed lights.the knobs could be changed out for handles and in a different finish to give the kitchen a fresher look.